Angles of Triangles Quick Check
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Question
Use the image to answer the 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
92°
92 degrees
38°
38 degrees
52°
52 degrees
232°
To find the measure of angle b, we can use the fact that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
Given that the exterior angle at angle a measures 142 degrees, we can set up the equation:
angle a + angle b = 142
Since angle a is labeled, we can substitute the value given for the exterior angle:
a + angle b = 142
Substituting in the value of angle a:
142 + angle b = 142
Simplifying the equation:
angle b = 0
Therefore, angle b measures 0 degrees.