Identify Angle Pair Relationships formed by a line

• Identify Angle Pair Relationships formed by a line. • • • Adjacent Angles Vertical Angles Linear Pair Complementary Angles Supplementary Angles

Do not COPY!! (def) An ACUTE ANGLE is an angle w/ a MEASURE less than 90° (def) A RIGHT ANGLE is an angle w/ a MEASURE = 90° (def) An OBTUSE ANGLE is an angle w/ a MEASURE greater than 90° but less than 180 °. (def) A STRAIGHT ANGLE is an angle w/ a MEASURE = 180° Interior of angle Exterior of angle

Draw a Acute Angle and write the definiti

Draw a Obtuse and Right Angle, and write the definition:

To Name an Angle- either use 3 letters or number it, never use only 1 letter unless there is only one angle with that vertex. If you use three letters, the vertex must be the middle letter. A D or never use 1 B E in this type of problem since more than one angle has a vertex of B.

(def)An ANGLE BISECTOR is a ray that divides an angle into 2 congruent angles. (def) ADJACENT ANGLES are 2 coplanar angles that share a common ray and vertex but no common interior pts. A D B C

ANGLE ADDITION POSTULATE- If D is in the interior of , then A D B C i. e. The sum of the parts = whole

(def) SUPPLEMENTARY ANGLES are 2 angles whose measures have a sum of 180° or 145° 35°

(def) COMPLEMENTARY ANGLES are 2 angles whose measures have a sum of 90° or 50° 40°

What is supplementary and complementary an Give example and definition:

(def) LINEAR PAIR ANGLES are 2 adjacent angles whose non-common sides form a line. Linear Pair Theorem- If 2 angles form a linear pair, then they are supplementary.

Vertical Angles Theorem- If 2 angles are vertical angles, then they are congruent. (def) VERTICAL ANGLES are 2 nonadjacent angles formed by intersecting lines

What is Vertical Angles Theorem and Linear Pair Theorem, Give example and defin

COPY IT

EXAMPLE 1 Identify all of the linear pairs and all of the vertical angles in the figure at the right. SOLUTION To find vertical angles, look or angles formed by intersecting lines. ANSWER 1 and 5 are vertical angles. To find linear pairs, look for adjacent angles whose noncommon sides are opposite rays. ANSWER 1 and 4 are a linear pair. are also a linear pair. 4 and 5

EXAMPLE 2 ALGEBRA Two angles form a linear pair. The measure of one angle is 5 times the measure of the other. Find the measure of each angle. SOLUTION Let x° be the measure of one angle. The measure of the other angle is 5 x°. Then use the fact that the angles of a linear pair are supplementary to write an equation. x + 5 x = 180° 6 x = 180° x = 30° ANSWER The measures of the angles are 30° and 5(30)° = 150°.

You Do The measure of an angle is twice the measure of its complement. Find the measure of each angle. SOLUTION Let x° be the measure of one angle. The measure of the other angle is 2 x° then use the fact that the angles and their complement are complementary to write an equation x° + 2 x° = 90° 3 x = 90 x = 30 ANSWER Write an equation Combine like terms Divide each side by 3 The measure of the angles are 30° and 2( 30 )° = 60°

To find the complement of an angle that measures x°, do by subtracting its measure from 90°, or (90 – x)°. To find the supplement of an angle that measures x°, do by subtracting its measure from 180°, or (180 – x)°.

Find the measure of each of the following. A. complement of F (90 – x) 90 – 59 = 31 B. supplement of G (180 – x) 180 – (7 x+10) = 180 – 7 x – 10 = (170 – 7 x)

Find the measure of each of the following. A. complement of F (90 – x) 41 90 – 41 = 49 B. supplement of G (180 – x) 180 – (4 x-5) = 180 – 4 x + 5 = (185 – 4 x) (4 x-5)

An angle is 10° more than 3 times the measure of its complement. Find the measure of the complement. Step 1 Let m A = x°. Then B, its complement measures (90 – x)°. Step 2 Write and solve an equation. x = 3(90 – x) + 10 Substitute x for m A and 90 – x for m x = 270 – 3 x + 10 Distrib. Prop. x = 280 – 3 x Combine like terms. Divide both sides by 4. 4 x = 280 x = 70 Simplify. The measure of the complement, B, is (90 – 70) = 20.

An angle is 15° more than 5 times the measure of its complement. Find the measure of the complement. Step 1 Let m A = x°. Then B, its complement measures (90 – x)°. Step 2 Write and solve an equation. x = 5(90 – x) + 15 Substitute x for m A and 90 – x for m x = 450 – 5 x + 15 Distrib. Prop. x = 465 – 5 x Combine like terms. Divide both sides by 4. 6 x = 465 x = 77. 5 Simplify. The measure of the complement, B, is (90 – 77. 5) = 12. 5.

Solve for x and find each angle measurement. 4 x +8 6 x - 42

Solve for x and find each angle measurement. 3 x - 5 6 x + 34

Solve for x and find each angle measurement.

Solve for x and find each angle measurement. (2 x – 7) 4 x - 10

Find a Missing Angle Measure The two angles below are supplementary. Find the value of x. 155 + x = 180 = Write an equation. Subtract 155 from each side. Simplify. Answer: 25

The two angles below are complementary. Find the value of x. x = 35 1. 2. 3. 4. A B C D

Find a Missing Angle Measure Find the value of x in the figure. Use the two vertical angles to solve for x. 68 + x = 90 – 68 =– 68 x = 22 Answer: 22 Write an equation. Subtract 68 from each side. Simplify.