Question

Find the value of x in each case:

Answer 1

45°

Explanation:

The sum of a triangle's angles is 180°.

Let's take the triangle FIG and try to express its angles in function of x.

● < F :

< F +3x = 180 => <F = 180 -3x

● < G :

IK and GH are paralell. IG is crossing them.

x and G are interior alternate angles so they have the same size.

< G = x

● < I :

We khow that < F = 180 -3x and < G = x

< I = 180-(< F + < G )

< I = 180 - ( 180-3x +x)

< I = 180 -(180-2x)

< I = 180 -180 +2x

< I = 2x

■■■■■■■■■■■■■■■■■■■■■■■

< F = 180 -3x

< G = x

< I = 2x

< I + > I + x + 2x = 360

2x + 180-x +3x = 360

4x + 180 = 360

4x = 180

x = 45°

●●●●●●●●●●●●●●●●●●●●●●●

Let's verify :

< F = 180 - 3*45 = 45 °

<G = x = 45°

< I = 2x = 90°

90° +45°+45° = 180°

So it's true.