Question

If ∠JLK = 130° and ∠KLM = 70°, what is the measure of the exterior angle at vertex K?

a. 130°
b. 70°
c. 110°
d. 360°

Answer 1

The measure of the exterior angle at vertex K is -20°.

Step-by-step explanation:

To find the measure of the exterior angle at vertex K, we need to use the fact that the sum of the measures of the interior angles of a triangle is always 180 degrees. In this case, the triangle is formed by ∠JLK, ∠KLM, and the exterior angle at vertex K. So we have:

∠JLK + ∠KLM + Exterior angle at vertex K = 180°

Plugging in the given values:

130° + 70° + Exterior angle at vertex K = 180°

Simplifying the equation, we get:

200° + Exterior angle at vertex K = 180°

Subtracting 200° from both sides, we get:

Exterior angle at vertex K = 180° - 200°

Exterior angle at vertex K = -20°

Therefore, the measure of the exterior angle at vertex K is -20°.