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

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°

Answer 1

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°.