Question

In this figure, ∠1 and ∠2 are located on a line.

Let m∠1=x° and m∠2=(14x)°.

What is the value of x?

Enter your answer in the box.

Answer 1

x = 144°

Explanation:

Since the larger line is a straight line, ∠1 and ∠2 are a linear pair. A linear pair is such a pair where two angles sum up to 180°.

⇒ ∠A + ∠B = 180°

Substitute the measure of ∠A and ∠B

⇒ x + x/4 = 180° [∠A = x; ∠B = x/4]

⇒ 4x/4 + x/4 = 180° [Rewrote x as 4x/4]

⇒ 5x/4 = 180°

Using cross multiplication

⇒ 5x = 180 × 4 = 720

⇒ x = 720/5 = 144°

Answer 2

In a straight line, all angles sum up to 180°

====================================

`\hookrightarrow \sf x +(1)/(4) x = 180`

`\hookrightarrow \sf (4x)/(4) +(1)/(4) x = 180`

`\hookrightarrow \sf (4x+x)/(4) = 180`

`\hookrightarrow \sf 4x+x= 180(4)`

`\hookrightarrow \sf 5x= 720`

`\sf \hookrightarrow x = 144`