Question

The measure of ∠CGD is 5° greater than the measure of ∠BGC. What is the measure of ∠AGF?

Answer 1

The measure of angle AGF is
`59\°`

Explanation:

Let

x------> the measure of angle CGD

y------> the measure of angle BGC

we know that

`x+y+67\°=180\°` -----> equation A

`x=y+5\°` -----> equation B

Substitute equation B in equation A and solve for y

`y+5\°+y+67\°=180\°`

`2y=180\°-72\°`

`2y=108\°`

`y=54\°`

Find the value of x

`x=54\°+5\°=59\°`

The measure of angle CGD is
`59\°`

m<AGF=m<CGD -------> by vertical angles

therefore

The measure of angle AGF is
`59\°`