Question

Solve for x and y then find angle ABE

Answer 1

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

Step-by-step 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°