Page 43 - Math Course 2 (Book 2)

Lines and Angles

Find Measures of Angles Find Measures of Angles

Example Angles ABC and DEF are complementary.
If m∠ABC = x + 12 and m∠DEF = 2x – 9, find the
measure of each angle.

ALGEBRA A. m∠ABC = 29°; m∠DEF = 61°
Angles PQR and STU are supplementary. B. m∠ABC = 41°; m∠DEF = 49°
If m∠PQR = x – 15 and m∠STU = x – 65, find the C. m∠ABC = 59°; m∠DEF = 121°
measure of each angle. D. m∠ABC = 71°; m∠DEF = 109°

Step 1 Find the value of x.

m∠PQR + m∠STU = 180° Supplementary angles

(x – 15) + (x – 65) = 180° Substitution

2x – 80 = 180° Combine like terms.

2x = 260° Add 80 to each side.

x = 130° Divide each side by 2.

Step 2 Replace x with 130 to find the measure of
each angle.

m∠PQR = x – 15 m∠STU = x – 65
= 130 – 15 or 115 = 130 – 65 or 65

m∠PQR = 115°
Answer Answer
m∠STU = 65°

Your Turn!

Real World Example

SEWING
Linda cuts a piece of material from the corner at a
35° angle. What is the measure of the other angle
formed by the cut?

A. 145°
B. 90°
C. 55°
D. 35°

Answer

35