To find angle b, we can use the property that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Since the exterior angle formed by angle a is 142 degrees, the sum of the measures of angles a and b is 142 degrees.
So, angle b = 142 degrees - angle a.
Since angle a is not given in the problem, we cannot determine the exact value of angle b without knowing the value of angle a.
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
232°
232 degrees
38°
38 degrees
52°
5 answers
Use the properties of exterior angles of triangles to find angle b.
(1 point)
Responses
92°
92 degrees
232°
232 degrees
38°
38 degrees
52°
(1 point)
Responses
92°
92 degrees
232°
232 degrees
38°
38 degrees
52°
Since the exterior angle formed by extending the line from angle a is 142 degrees, and the sum of the measures of the remote interior angles of a triangle is equal to the measure of the exterior angle, we can set up an equation:
angle a + angle b = 142
Since angle a is not given in the problem, we cannot determine the exact value of angle b without knowing the value of angle a.
Therefore, none of the given options (92°, 232°, 38°, 52°) can be determined as the correct answer.
angle a + angle b = 142
Since angle a is not given in the problem, we cannot determine the exact value of angle b without knowing the value of angle a.
Therefore, none of the given options (92°, 232°, 38°, 52°) can be determined as the correct answer.
then how
Since the exterior angle formed by extending the line from angle a is 142 degrees, and the sum of the measures of the remote interior angles of a triangle is equal to the measure of the exterior angle, we can set up an equation:
angle a + angle b = 142
To find angle b, we need to know the measurement of angle a. Without that information, we cannot determine the exact value of angle b.
Therefore, the correct response would be that angle b cannot be determined with the given information.
angle a + angle b = 142
To find angle b, we need to know the measurement of angle a. Without that information, we cannot determine the exact value of angle b.
Therefore, the correct response would be that angle b cannot be determined with the given information.
1 answer