Warm Up:

Solve for the variable:1. 105 = 2x + 5

50

2. 119 – x = 3x + 1127

3. 2x – 7 = -4x + 1

Linear Pair

I: Two angles that share a common vertex and together make a straight line (180°).

M: What is the missing measure?

Vertical Angles

I: Two angles that share a common vertex and are opposite of each other when two lines cross. Angles will always be congruent.

M:

Acute Angle

I: Has a measure between 0° and 90°.

M: 67°

Right Angle

I: An angle that has a measure equal to 90°.

M:

Obtuse Angle

I: An angle that has a measure between 90° and 180°.

M:

140°

Complementary Angles

I: A pair of angles whose sum of measures equals 90°.

M: Find the missing measure.

58°

x°

Supplementary Angles

I: A pair of angles whose sum of measures equals 180°.

M: Find the value of x.

x x + 60

Angle Bisector

I: A ray (or line segment) that divides an angle into two congruent angles.

M:

Practice

are complementary. Solve for x and the measure of both angles. 1. = 5x + 2 2 = 2x + 4 x = 12; = 62° and 2 = 28°

2. = 12x + 4 = 9x + 2

x = 4; = 52° and 2 = 38°

One of two complementary angles is 16 degrees less than its complement. Find the measure of both angles.

Two angles: x and x – 16

X = 53

X – 16 = 37

One of two supplementary angles is 98° greater than its supplement. Find the measure of both angles.

Two Angles: x and x + 98

X = 41X + 98 = 139

5. One of two complementary angles is 57° greater than twice its complement. Find the measure of both angles.

Two Angles: x and 2x + 57

X = 112x + 57 = 79

6. One of two supplementary angles is 123° less than twice its supplement. Find the measure of both angles.

Two angles: x and 2x – 123

X = 101 2x – 123 = 79

7. Find all missing angle measures

Given: m1 = 90°, m2 = 34°, and m6 = 137°

4 =

5 =

7 =

8 =

90°

34°

137°

90°

146

°

146

°

137

°

43°

1 and 2 are complementary angles, state the numerical value of x.

8. m1 = 2x, m2 = 3xX = 18

9. m1 = 30 + x, m2 = 40 + xx = 10

3 and 4 are supplementary angles, state the numerical value of y.

10. m3 = 2y, m4 = 3y – 15 y = 39

11. m3 = 5m4, m4 = yy = 30