# Unknown Angles Complementary Supplementary Angles Equations B M

Unknown Angles Complementary Supplementary Angles & Equations B+ M A TH WORD WALL M I S S HA Z E N

Complementary Angles Definition Using a Diagram Word Problems

a˚ Definition: Two Angles are Complementary when they add up to 90 degrees (a Right Angle). They don't have to be next to each other, just so long as the total is 90 degrees. b˚ a + b = 90˚

Diagrams Sometimes, the best way to solve a problem is to draw the picture. (It’s okay if the angles aren’t perfect) Example: One angle is four times larger than its complement. What is the measure of the smaller angle? x = the smaller angle 4 x + x = 90˚ *Find the larger angle 5 x = 90˚ by plugging in x. 5 5 4 x˚ x = 18˚ x˚ The smaller angle is 18˚.

Your Turn! Use a piece of scrap paper to help you solve the problem below. You can go back to the diagram page for help! One angle is two times larger than its complement. What is the measure of the larger angle? a) 30˚ b) 45˚ c) 60˚ d) 120˚

Try Again! 30˚ is the size of the smaller angle, how do you use that to find the size of the larger angle?

Try Again! 45˚ is the size of the angles if both angles were the same size.

Great! The larger angle = 60 because: 2 x + x = 90˚ 3 x = 90 ˚ 3 3 x = 30 ˚ 2(30 ˚) = 60 ˚ Try the next question.

Try Again! The angle would be 120˚ if both angles were to be supplementary and set to equal 180 ˚

Question 2 Use a piece of scrap paper to help you solve the problem below. You can go back to the diagram page for help! One angle is two more than seven times larger than its complement. What is the measure of the smaller angle? a) 11˚ b) 11. 25˚ c) 77˚ d) 79˚

Try Again! 11˚ is the size of the smaller angle when you set up: 7 x + 2 + x = 90 How do you use that to find the size of the larger angle?

Try Again! 11. 25˚ is the size of the smaller angle when you set up without including the two more than, it should look like: 7 x + 2 + x = 90 How do you use that to find the size of the larger angle?

So Close! You knew x = 11, but you forgot to add the extra 2 The larger angle = 7 x + 2

Great! The larger angle = 79 because: 7 x + 2 + x = 90˚ 8 x + 2 = 90 ˚ -2 8 x = 88˚ 8 8 x = 11 7(11) + 2 = 79 ˚

Supplementary Angles Definition Using a Diagram Word Problems

a˚ Definition: Two Angles are Supplementary when they add up to 180 degrees (a Straight Angle). They don't have to be next to each other, just so long as the total is 180 degrees. b˚ a + b = 180˚

Diagrams Sometimes, the best way to solve a problem is to draw the picture. (It’s okay if the angles aren’t perfect) Example: One angle is eight more than three times its supplement. What is the measure of the smaller angle? x = the smaller angle 3 x + 8 + x = 180˚ 4 x + 8 = 180˚ -8 4 x = 172 (3 x + 8)˚ x˚ 4 4 x = 43˚ The smaller angle is 43˚.

Your Turn! Use a piece of scrap paper to help you solve the problem below. You can go back to the diagram page for help! One angle is two times larger than its supplement. What is the measure of the smaller angle? a) 30˚ b) 60˚ c) 90˚ d) 180˚

Try Again! 30˚ is the size of the smaller angle if you set the equation equal to 90 instead of 180

Great! The smaller angle = 60 because: 2 x + x = 180˚ 3 x = 180 ˚ 3 3 x = 60 ˚ Try the next question.

Try Again! 90˚ is the size of the angles if both angles were the same size

Try Again! The sum of both angles should be set to equal 180 ˚ 2 x + x = 180

Question 2 Use a piece of scrap paper to help you solve the problem below. You can go back to the diagram page for help! One angle is nine less than six times its supplement. What is the measure of the larger angle? a) 27˚ b) 34. 2˚ c) 153˚ d) 162˚

Try Again! x = 27˚ is the size of the smaller angle when you set up without including the two more than, it should look like: 6 x – 9 + x = 180 How do you use that to find the size of the larger angle?

Try Again! Be sure you set it up as nine less than 6 x 6 x – 9 + x = 180

Great! The larger angle = 153 because: 6 x – 9 + x = 180˚ 7 x – 9 = 180 ˚ +9 7 x = 189˚ 7 7 x = 27 6(27) – 9 = 153 ˚

So Close! You knew x = 27, but you forgot to subtract 9 when you plugged x in The larger angle = 6 x – 9

Angles & Equations Angle Relationships Identify Missing Angles

Angles Relationships Angle on a Line Angles at a Point

Angles at a Point Click the statements that are true about the angles on a line below? (There may be more than one possible answer) x I H x N P J M L K x

Angles on a Line Click the statements that are true about the angles on a line below? (There may be more than one possible answer) x x D A B E C x x

Identifying Missing Angles A B F O 32˚ E D C a) 32˚ b) 58˚ c) 90˚ d) 148˚

Great! Try the Next Question

Try Again! Recall the definition of vertical angles

Question 2 A B F O 32˚ E D C a) 32˚ b) 58˚ c) 90˚ d) 148˚

Great! Try the Next Question

Try Again!

Question 3 G F H 2 x + 8 4 x – 1 x– 2 O J a) 23˚ b) 25˚ c) 58˚ d) 99˚

Great! Try the Next Question

Try Again!

Question 4 A B F x˚ 2 x˚ x˚ H E D C a) 22. 5˚ b) 45˚ c) 90˚ d) 180˚

Great! x = 45 because: 2 x + x + x + x = 360˚ 8 x = 360 ˚ 8 8 x = 45 2(45) = 90 ˚

Try Again! Name all the values of vertical angles and remember the total sum of angles at a point.

Vocabulary Acute Angles Adjacent Angles Obtuse Angles Vertical Angles Right Angles on a Line Straight Angles at a Point Perpendicular

Acute Angles angles that measure less than 90˚

Obtuse Angles angles that measure greater than 90˚ but less than 180˚

Right Angles angles that measure exactly 90˚

Straight Angles angles that measure exactly 180˚

Adjacent Angles angles that share a side (they are next to each other) b˚ a˚ c˚ a + b = c

Vertical Angles two nonadjacent angles formed by intersecting lines a˚ b˚ a = b

Angles on a Line the sum of angle measurements that form a line b˚ a˚ c˚ a + b + c = 180˚

Angles at a Point the sum of the measurements of angles that share a vertex (together angles form a circle) b˚ a˚ a + b + c = 360˚ c˚

Perpendicular lines that intersect at 90˚

Helpful Hint: Solving for x: In the example below, click on the information used to identify the variable. In a pair of complementary angles, the measurement of the larger angle is twice the size of the smaller angle. What is the measure of the smaller angle?

Awesome! x = the measure of the smaller angle

Try Again

Assessment Question 1: Set up and find the value of x. x˚ 77˚ a) 13˚ b) 35˚ c) 53˚ d) 103˚ x x x Next Question

Assessment Question 2: Set up and find the value of x. 35˚ x˚ 35˚ xa) 20˚ xb) 35˚ c) 55˚ xd) 125˚ Next Question

Assessment Question 3: An angle is twenty-one more than twice its supplement. What is the measure of the smaller angle? a) 53˚ b) 37˚ c) 23˚ d) 67˚ x x x Next Question

Assessment Question 4: Set up and find the value of x. x˚ 17˚ 30˚ xa) 43˚ xb) 47˚ c) 133˚ xd) 137˚ Next Question

Assessment Question 5: Set up and find the value of x. x˚ 2 x˚ xa) 18˚ b) 36˚ xc) 60˚ xd) 72˚ Next Question

Assessment Question 6: An angle measures fourteen less than its complement. What is the measure of the smaller angle? a) 38˚ b) 52˚ c) 133˚ d) 147˚ x x x Next Question

Assessment Question 7: Set up and find the value of x. x˚ 4 x˚ 160˚ a) 14˚ b) 18˚ c) 70˚ d) 155˚ x x x Great Job! How many did you get right on the first try?

Fantastic!

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