Question

An angle measures 84° more than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

48°

132°

Explanation:

Let the measure of one angle be x°

So, Measure of supplementary angle = (x + 84)°

x° +(x +84)° = 180°

(2x + 84)° = 180°

2x + 84 = 180

2x = 96

x = 96/2

x = 48°

(x + 84)° = 48 + 84 = 132°

Answer 2

Let ∠1 be x

Let ∠2 be x+84

ATQ,

`\rm\:x+x+84= 180 \degree`

`\rm \: 2x + 84 = 180`

`\rm \: 2x = 180 - 84`

`\rm \: 2x = 96`

`\boxed{ \bf \: x=48 \degree}`

So,

`\begin{gathered} \sf \: ∠1 = x \\ \sf \: = 48 \degree\end{gathered}`

`\begin{gathered} \sf \: ∠2 = x+84 \\ \sf = \: 48+84 \\ \sf∠2 = 132 \degree\end{gathered}`

• Remember that:
• Supplementary angles sums upto 180°
• Complementary angles sums upto 90°