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How do I solve this?

How do I solve this?-example-1
User Doug
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1 Answer

3 votes

Answer:


x=9\\y=41\\m\angle EBF = 56^\circ

Explanation:

Finding x is not too bad since it's clear that
\angle ABD and
\angle DBC are complementary angles, which add up to 90°:


m\angle ABD+m\angle DBC=90^\circ\\(3x+7)^\circ+(5x+11)^\circ=90^\circ\\3x+7+5x+11=90\\8x+18=90\\8x=72\\x=9

Given we now know the value of x, we can use that information to solve for y by recognizing that
\angle DBC and
\angle FBC are supplementary angles, which add up to 180°:


m\angle DBC+m\angle FBC=180^\circ\\(5x+11)^\circ+(3y+1)^\circ=180^\circ\\5x+11+3y+1=180\\5(9)+11+3y+1=180\\45+11+3y+1=180\\3y+57=180\\3y=123\\y=41

Lastly, we can figure out
m\angle EBF since both that and
\angle DBC are vertical angles, meaning they have the same angle measure. Since
m\angle DBC=(5(9)+11)^\circ=(45+11)^\circ=56^\circ, then
m\angle EBF=56^\circ as well.

I hope this helped! Feel free to comment below if I need to expand on anything that you may have not understood.

User Ankur Mahajan
by
8.4k points

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