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°
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.
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°
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.
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.
To find angle b in the right triangle, we can use the property of exterior angles of triangles. According to this property, the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
In this case, the exterior angle formed by extending the line from angle a is 142 degrees. We need to find angle b, which is one of the remote interior angles of the right triangle.
Since angle b is a remote interior angle to the exterior angle of 142 degrees, we can calculate its measure by subtracting 142 degrees from 180 degrees (which is the sum of the measures of the two non-right angles in the triangle).
So, angle b = 180 degrees - 142 degrees = 38 degrees.
Therefore, the correct answer is 38 degrees.
To find angle b, we can use the fact that the sum of the measures of the remote interior angles of a triangle is equal to the measure of the exterior angle.
In this case, the measure of the exterior angle is given as 142 degrees.
Since the exterior angle is formed by the extension of angle a, we can conclude that the sum of angle a and angle b is equal to 142 degrees.
Let's set up an equation to solve for angle b:
angle a + angle b = 142
Since angle a is not given, we cannot solve for angle b with the information provided.