Question

I need help , if yk the answer help fr!!!

Answer 1

Answer:

The measure of the angle JKG is:

m∠JKG = 56°

Step-by-step explanation:

Given

m∠JKG = 76-2x

m∠FHK = 6x-4

J is a midpoint of the segment FG and K is a midpoint of the segment GH.

To determine

m∠JKG = ?

Given that J is a midpoint of the segment FG and K is a midpoint of the segment GH. Thus, making two similar triangles, ΔJGK and ΔFGH

We know that two triangles are similar if the only difference is size. So, the angles remain the same.

so m∠JKG and m∠FHK are equal.

i.e.

m∠JKG = m∠FHK

substitute m∠JKG = 76-2x and m∠FHK = 6x-4

76-2x = 6x-4

6x+2x = 76 + 4

8x = 80

divide both sides by 8

8x/8 = 80/8

x = 10

Therefore, the value of x = 10

As

m∠JKG = 76-2x

substitute x = 10

m∠JKG = 76 - 2(10)

             = 76 - 20

             = 56°

Therefore, measure of the angle JKG is:

m∠JKG = 56°