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Solve for x and y then find angle ABE

Solve for x and y then find angle ABE-example-1
User Imcoddy
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1 Answer

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Answer: x is 9° , y is 21°. The measure of angle ABE is 48°.

Explanation:

First we will solve for x.

The variable x appears in the angle 8x + 18 and that angle is a right angle.

Right angles have the measure of 90 degrees so we will set the angle equal 90 and solve for x.

8x + 18 = 90 Subtract 18 from both sides

- 18 -18

8x = 72 divide both sides by 8

x = 9

y is also on the right side and the combination of both angles has to also equal 90 degrees because they form a right angle.

Since we already know x is 9 we will input it into the left side for x and solve for y.

y + 3(9) + 2y = 90

3y + 27= 90

-27 -27

3y = 63

y = 21

Now we need to find the measure of angle ABE.

ABE is represented by y + 3x so since we know the value of y and x we will input it into the expression and solve for the angle.

21 + 3(9) = m∠ABE

21 + 27= m∠ABE

48 = m∠ABE

This means the measure of angle ABE is 48°

User Daniel Tadros
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