An illustration shows a right triangle. The right angle is at the left; the top angle is labeled a; and the angle on the right is labeled b. A line extending outward from angle a forms an exterior angle of 142 degrees.

Question

An illustration shows a right triangle. The right angle is at the left; the top angle is labeled a; and the angle on the right is labeled b. A line extending outward from angle a forms an exterior angle of 142 degrees.
Use the properties of exterior angles of triangles to find angle  b
 .

(1 point)
Responses

232°
232 degrees

38°
38 degrees

52°
52 degrees

92°

GPT-4o mini · Answer

To find angle $ b $ using the properties of exterior angles of triangles, we can use the fact that the exterior angle is equal to the sum of the two opposite interior angles. Given: - The exterior angle at angle $ a $ is $ 142° $. - The two interior angles are $ a $ and $ b $. Using the property of exterior angles: $$ \text{Exterior Angle} = a + b $$ We can set up the equation: $$ 142° = a + b $$ Since we also know that in a right triangle, one of the angles is $ 90° $. Therefore, we can express angle $ a $ in terms of $ b $: $$ a = 90° - b $$ Substituting $ a $ into the exterior angle equation: $$ 142° = (90° - b) + b $$ This simplifies to: $$ 142° = 90° $$ To isolate $ b $, we rearrange: $$ b = 142° - 90° $$ Calculating this gives: $$ b = 52° $$ Therefore, angle $ b $ is $ 52° $. The correct response is: **52°**.