Question

Among the two supplementary angles,the measures of the larger angle is 36° more than the measures of smaller. find their measures​

Answer 1

To Find:-

• The measure of the angles

Given:-

• Two supplementary angles,the measures of the larger angle is 36° more than the measures of smaller

Solution:-

We know that supplementary angle measures 180°

Method 1

Let the angles one angle be x and the other be( x+ 36 )

So,

⟹ x + x + 36 = 180

⟹ 2x + 36 = 180

⟹ 2x = 180 - 36

⟹ 2x = 144

⟹ x = 144/2

⟹ x = 72°

∴ The smaller angle is 72° and the larger angle is

= ( x + 36 )°

= ( 72 + 36 )°

= 108°

Method 2

Let the angles be x and ( 180 - x )

So,

⟹ x = ( 180 - x ) + 36

⟹ x + x = 180 + 36

⟹ 2x = 216

⟹ x = 216/2

⟹ x = 108°

∴ The smaller angle is ( 180 - x )

= ( 180 - 108 )°

= 72°

and the larger angle is 108°

Now, Verification

⟹ 108° + 72° = 180°

⟹ 180° = 180°

L.H.S = R.H.S

Hence, Proved.