Question

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

Answer 1

Answer:

The measure of angle AGF is  $59\°$

Step-by-step 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  $59\°$