FINDING MISSING ANGLE MEASURES PART 1 LEARNING TARGET

FINDING MISSING ANGLE MEASURES PART 1

LEARNING TARGET 2 Use the definitions and relationships of complementary, supplementary, adjacent, and vertical angles to determine missing angle measures.

VERTICAL ANGLES Let’s Review…Vertical Angles are not adjacent, are formed by two intersecting lines, and are congruent (equal). Angles A and B are Vertical and therefore the same angle measure.

VERTICAL ANGLES We can use the definition of Vertical Angles to find the measures of other angles. How to Find the Missing Angle Measure: All vertical angles are congruent (equal) and therefore equal to each other. If Angle A is 35°, then Angle B is also 35°.

VERTICAL ANGLES Find the angle measure of each missing angle.

COMPLEMENTARY ANGLES Let’s Review…Complementary Angles are two angles whose sum is 90°. b a

COMPLEMENTARY ANGLES How to Find the Missing Angle Measure: Calculate the measure of the missing angle so that the sum of the two angles equals 90°. 27° + b = 90° b = 63°

COMPLEMENTARY ANGLES Find the measure of the missing angle.

SUPPLEMENTARY ANGLES Let’s Review…Supplementary Angles are two (or more) angles whose sum is 180°. a b

SUPPLEMENTARY ANGLES How to Find the Missing Angle Measure: Calculate the measure of the missing angle so that the sum of the two angles equals 180°. 155° + b = 180° b = 25°

SUPPLEMENTARY ANGLES Find the measure of the missing angle.

SUPPLEMENTARY ANGLES Find the Supplement of each angle. Angle Supplement Your Angle + X = 180° 50° 130° 110° 70° 65° 115° 26° 154°

COMPLEMENTARY ANGLES Find the Complement of each angle. Angle Complement Your Angle + X = 90° 50° 40° 110° Impossible 65° 26° 64°

TIME TO PRACTICE

1)FIND Find. THE the. MISSING missing. ANGLE angle. ? ° 36°

1)FIND Find. THE the. MISSING missing. ANGLE angle. ? ° 36° Relationship: Complementary 90° – 36° = 54°

2)FIND Find. THE the. MISSING missing. ANGLE angle. ? ° 64°

2)FIND Find. THE the. MISSING missing. ANGLE angle. ? ° 64° Relationship: Complementary 90 ° – 64° = 26°

5)FIND Find. THE the. MISSING missing. ANGLE angle. ? ° 168 °

5)FIND Find. THE the. MISSING missing. ANGLE angle. ? ° Relationship: Supplementary 180° – 168° = 12° 168 °

6)FIND Find. THE the. MISSING missing. ANGLE angle. 58° ? °

6)FIND Find. THE the. MISSING missing. ANGLE angle. 58° Relationship: Supplementary 180° – 58° = 122° ? °

FIND THE MISSING ANGLE ? º 35º

FIND THE MISSING ANGLE ? º 35º Relationship: Vertical 35° = 35°

FIND THE MISSING ANGLE ? º 140º

FIND THE MISSING ANGLE ? º 140º Relationship: Vertical 140° = 140°

FINDING A MISSING ANGLE AND X Part 2

FINDING THE MISSING ANGLE…WITH X. Sometimes the lines between Geometry and Algebra blur just a bit. For example, sometimes the missing angle is not just a letter but a problem to be solved. Let’s take a look. We know that the two angles are supplementary…but how do we solve for X. When we solve these types of problems we are going to have TWO ANSWERS…what does X equal and what is the measure of the missing angle.

FIND THE MISSING ANGLE AND X We begin by figuring out what the two angles need to equal when added together. In this case… 180° Angle 1 + Angle 2 = 180 30 + 2 x = 180 (We can solve this…no problem) 2 x = 150 X = 75 So the angle is 2 x = 2(75) = 150°

Solve for x. AND X FIND THE 3)MISSING ANGLE 2 x° 3 x° What is the relationship? What do the two terms need to equal?

Solve for x. AND X FIND THE 3)MISSING ANGLE 2 x°= 2(18) = 36° 2 x° 3 x° = 3(18) = 54° 3 x° + 2 x° = 90° 5 x = 90 x =18

Solve for x. AND X FIND THE 7)MISSING ANGLE 4 x° 5 x° What is the relationship? What do the two terms need to equal?

Solve for x. AND X FIND THE 7)MISSING ANGLE 5 x° = 5(20) = 100° 4 x° = 4(20) = 80° 4 x° + 5 x° = 180° 9 x° = 180° x = 20 5 x°

Solve for x. AND X FIND THE 8)MISSING ANGLE X = 30 2(30) + 10 = 70° 2 x + 10 X = 30 3(30) + 20 = 110° 3 x + 20 (2 x + 10) + (3 x + 20) = 180 Like Terms Combine 5 x + 30 = 180 Solve for X 5 x = 150 x = 30

Solve for x. AND X FIND THE 4)MISSING ANGLE x + 25 2 x + 5 What is the relationship? What do the two terms need to equal?

Solve for x. AND X FIND THE 4)MISSING ANGLE X = 20 20 + 25= 45 X = 20 2(20) + 5 = 45 (2 x + 5) + (x + 25) = 90 Terms 3 x + 30 = 90 3 x = 60 x + 25 2 x + 5 Combine Like Solve for X

FIND THE MISSING ANGLE AND X