A figure with parallel lines m and n is shown. What is the measure, in degrees, of angle b?

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Lilystephens67 Lilystephens67

01-02-2020
Mathematics

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A figure with parallel lines m and n is shown. What is the measure, in degrees, of angle b?

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theleangreenbean theleangreenbean · Answer 1 · 2022-05-19T20:41:57+02:00

Answer:

The measure of angle b is 42 degrees.

Step-by-step explanation:

We can assume that lines m and n are parallel.

Look at the triangle. Specifically, look at the angle in the triangle that is NOT the right angle or angle b.

This angle is the alternate exterior angle of the angle that measures 48 degrees.

Alternate exterior angles always have the same measure. Therefore, the measure of this angle in the triangle is 48 degrees as well.

The interior angles of triangles always have a sum of 180 degrees. To find angle b, subtract 90 and 48 degrees from 180 degrees:

180 - 90 - 48 = 42

Therefore, angle b is 42 degrees.

vipinkumar69547 vipinkumar69547 · Answer 2 · 2022-05-20T07:12:31+02:00

The measure, in degrees, of the angle b, is 42°.

What is known as the alternate exterior angle theorem?

The alternate exterior angle theorem states that when two lines are parallel to each other and another line is passing through it, the alternate exterior angles produced by it as equal.

From the figure, we can see that the alternate exterior angles are 48° and the angle inside the triangle. Therefore that angle is also equal to 48°.

The other angles inside the triangle are 90° and b.

Now, we can use the triangle angle sum theory to find the value of b.

b + 48° + 90° = 180°

⇒ b + 138° = 180°

⇒ b = 42°

Therefore. we have found the measure, in degrees, of the angle b as 42°.

Learn more about alternate exterior angles here: https://brainly.com/question/2398628

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