Question

what is the total of the three exterior angles? a + b + c =
check
a =
b =

Explanation:

Step1: Find value of a

Use the property that the sum of adjacent - interior and exterior angles of a triangle is 180°. For the angle adjacent to 140°, the interior angle is 180 - 140=40°. For the angle adjacent to 130°, the interior angle is 180 - 130 = 50°. In a triangle, the sum of interior angles is 180°. Let's consider the first non - overlapping triangle. The third interior angle of this triangle is 180-(40 + 50)=90°. Then, since a and the 90° angle are adjacent, a = 90°.

Step2: Find value of b

In the second non - overlapping triangle, one interior angle is 65° and another is 61°. The third interior angle of this triangle is 180-(65 + 61)=54°. Then, since b and the 54° angle are adjacent, b = 126°.

Step3: Find value of c

The interior angle adjacent to c in the second non - overlapping triangle is 65°. So c=115°.

Step4: Calculate a + b + c

a + b + c=90+126 + 115=331.

Answer:

a = 90, b = 126, a + b + c = 331