Question

use the figure for exercises 13 - 15. find the measure of the given angle. 13. a 14. b 15. c envision + geometry

Explanation:

Step1: Use the exterior - angle property of a triangle

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Find angle a

For the triangle with exterior angle 112° and non - adjacent interior angles a and 43°, we have 112°=a + 43°. So, a=112°−43° = 69°.

Step3: Find angle b

For the larger triangle, one of its exterior angles is related to the angles inside. We know that the sum of angles on a straight line is 180°. First, find the angle adjacent to 112° which is 180° - 112°=68°. Then, using the angle - sum property of a triangle in the triangle with angles 68°, 71°, and b, we know that the sum of interior angles of a triangle is 180°. So, b=180°-(68° + 71°)=41°.

Answer:

a = 69°
b = 41°