Question

If there are 2 supplementary angles <d and <r where m<d=(4x+8) and m<e=(x+17 and <f is. A vertical angle with <d what is the measure of <f

Answer 1

If angle <d is a supplementary angle with angle <r, then the sum of their measures is 180 degrees.

Let m<e = x + 17

And m<d = 4x + 8

Since <d and <f are vertical angles, they have equal measures.

So, m<d = m<f

Thus, we can equate the measures of <d and <r.

4x + 8 = 180 - (x + 17)

4x + 8 = 180 - x - 17

4x + x = 180 - 17 - 8

5x = 155

x = 31

m<f = m<d = 4(31) + 8 = 124 + 8 = 132 degrees.

Therefore, the measure of angle <f is 132 degrees.