Question

Find the value of x if GH and JH are both 13 units long. Justify your answer.

(7x + 5)º
(x+ 47)º​

This is Geometry
Angles of a triangle.

Answer 1

`x=7`

Explanation:

we have the triangle GHJ

If the segment side GH is equal to the segment JH

then

The triangle GHJ is an isosceles triangle

Remember that

An isosceles triangle has two equal interior angles and two equal sides

so

m∠G=m∠J

we have

m∠G=(7x+5)°

m∠J=(x+47)°

equate the equations

(7x+5)°=(x+47)°

Solve for x

`7x-x=47-5\\6x=42\\x=7`