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 angle - sum property of a triangle

The sum of interior angles of a triangle is 180°.

Step2: Find angle a

In the triangle with angles a, 71°, and 112° exterior - angle relationship. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let's first find the third angle of the triangle containing a. The angle adjacent to 112° is 180 - 112=68°. Then, for the triangle with angles a, 71°, and 68°, we have a + 71+68 = 180. So a=180-(71 + 68)=41°.

Step3: Find angle b

We know that the sum of angles on a straight line is 180°. Consider the straight - line where one angle is 33° and the other part is composed of a and b. So 33+a + b=180. Substitute a = 41° into the equation: 33+41 + b=180. Then b=180-(33 + 41)=106°.

Step4: Find angle c

For the triangle with angles 43°, 112° exterior - related angle (68° as calculated before), and c. Using the angle - sum property of a triangle, c+43 + 68=180. So c=180-(43 + 68)=69°.

Answer:

1. a = 41°
2. b = 106°
3. c = 69°