Question

In the diagram below, what is the value of x?

Answer 1

Answer: x = 43°

Explanation:

I have provided a picture to explain why x is 43°

∠AGF = 90°

∠CHF = 90°

∠BGJ = 47°

∠EGI = x°

Since ∠EGI and ∠FGJ are vertical angles that means they are congruent. So once we find the value of x ∠EGI = x° and ∠FGJ = x°

∠BGJ + ∠AGF + ∠FGJ = 180°

`47+90+x=180`

`137+x=180\\-137=-137\\x=43`

You could also just add ∠BGJ and ∠FGJ since they will equal to 90°

`47+x=90\\-47=-47\\x=43`

Answer 2

x = 43

Explanation:

let x be the angle between the right angle, 90° and 47°

these 3 angles lie on a straight line and sum to 180° , so

90 + x + 47 = 180

x + 137 = 180 ( subtract 137 from both sides )

x = 43