If m< EBC = 3y+10 and m< ABE = 2y-20, find m< EBF.

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facundo3141592 facundo3141592 · Answer 1 · 2022-09-22T18:18:46+02:00

By using the fact that EBC and ABE are supplementary angles, we will see that the measure of angle EBF is 106 degrees.

First, we can notice that angles EBC and ABE are supplementary angles, which means that their measures add up to 180°.

Then we can write:

m∠EBC + m∠ABE = 180°

Replacing what we know we get:

3y + 10 + 2y - 20 = 180°

Now we can solve this linear equation for y, we will get:

5y - 10 = 180

5y = 180 + 10

y = 190/5 = 38

Then we have that:

EBC = 3*38 + 10 = 124°

ABE = 2*38 - 20 = 56°

Now, in the image it says that:

ABE = 2b = 56°

then b = 56°/2 = 28°

And ABF = 7b - 24 = 162°

Then:

EBF = ABF - ABE = 162° - 56° = 106°

We conclude that the measure of angle EBF is 106 degrees.

If you want to learn more about supplementary angles:

https://brainly.com/question/2046046

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