Question

6 The measures of two angles are in the ratio 7: 8 and they are supplementary angles. What are their
measures in degrees?​

Answer 1

Answer:

84°, 96°

Step-by-step explanation:

Let the angles be 7x and 8x.

Since they are supplementary, their sum is 180°.

⇒ 7x + 8x = 180°

⇒ 15x = 180° ⇒ x = 12°

∴ 7x = 7 × 12 = 84°

  8x = 8 × 12 = 96°

Answer 2

• Given

• Ratio of two supplementary angles = 7 : 8

• To find

• The measure of each angle

• Solution

Let the two angles be 7x and 8x.

As we know,

• Sum of supplementary angles = 180°

⟶ 7x + 8x = 180°

⟶ 15x = 180°

⟶ x = 180°/15

⟶ x = 12°

The value of x = 12°

The measure of both the angles -

• 7x = 7 × 12° = 84°
• 8x = 8 × 12° = 96°

____________________________________

Let's verify -

Sum of the supplementary angles = 180°

Measure of both the supplementary angles = 84°, 96°

Their sum -

⟶ 84° + 96°

⟶ 180°

Hence, verified.