2-3 Additional Pracitce

Parallel Lines and Triangle Angle Sums

Exercises 13-15

13. The measure of a is 35°

14. The measure of b is 74°

15. The measure of c is 66°

Step-by-step explanation:

In the given figure

13.

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ 33° + 112° + a = 180°

→ Add the like terms in the left side

∴ 145° + a = 180

→ Subtract 145° from both sides

∵ 145° - 145° + a = 180° - 145°

∴ a = 35°

14.

∵ a, 71° and b formed a straight line

∵ The sum of the measures of the linear angles is 180°

∴ a + 71° + b = 180°

→ Substitute the value of a

∴ 35° + 71° + b = 180°

→ Add the like terms in the left side

∴ 106° + b = 180°

→ Subtract 106° from both sides

∵ 106° - 106° + b = 180° - 106°

∴ b = 74°

15.

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ 43° + 71° + c = 180°

→ Add the like terms in the left side

∴ 114° + c = 180°

→ Subtract 114° from both sides

∵ 114° - 114° + c = 180° - 114°

∴ c = 66°