Question

Two angles are supplementary. Three times the measure of one angle is 24° less than the measure of the other. What is the measure of each angle?​

Answer 1

Answer :-

• The measure of each angles are 51° and 93°.

Step-by-step explanation:

To Find :-

• The measure of angles.

Given that,

• Two angles are supplementary.
• Three times the measure of one angle is 24° less than each other.

⠀⠀⠀⠀⠀ ⠀⠀∴ [ 3x - 24 ]

Assumption :-

Let us assume the two angles angles as (x)° and (3x - 24)° ... given, respectively.

We know,

Supplementary angles measures 180°,

Therefore,

• (x)° + (3x - 24)° = 180°

⇒ (x) + (3x - 24) = 180

⇒ x + 3x - 24 = 180

⇒ 4x - 24 = 180

⇒ 4x = 180 + 24

⇒ 4x = 204

⇒ x = 204/4

⇒ x = 51

The value of x is 51.

Now, The measure of angles :-

• (x) = 51°
• (3x-24) = (3*51-24) = (153-24) = 93°

V E R I F I C A T I O N :-

• (x) + (3x - 24) = 180

By putting the values, of (x) and (3x - 24) in L.H.S :-

⇒ (x) + (3x - 24)

⇒ 51 + 93

⇒ 180

Now, L.H.S = R.H.S = 180

Hence, Verified!