Question

among two supplementary angles the measure of larger angle is 36 degree more than the measure of smaller find the angles​

Answer 1

• The larger angle = 112°
• The smaller angle = 68°

Given :–

• Two supplementary angles.
• The measure of larger angle is 36° more than of the smaller angle.

To Find :–

• The measures of both the angles.

Solution :–

Let,

The smaller angle be x.

The larger angle be x + 44° because according to the question, the measure of larger angle is 36° more than the measure of smaller angle.

We know that,

Sum of two supplementary angles = 180°

I.e.,

Smaller angle + larger angle = 180°

$\mapsto x + x + 44 \degree = 180 \degree$

$\mapsto 2x + 44 \degree = 180 \degree$

$\mapsto 2x = 180 \degree - 44 \degree$

$\mapsto 2x = 136 \degree$

$\mapsto x = \cancel{\dfrac{136 \degree}{2} }$

$\mapsto x = 68 \degree$

So,

Smaller angle = x = 68°

Larger angle = x + 44° = 68° + 44° = 112°

Hence,

The measures of the smaller and the larger angle is 68° and 112°.

Verification :–

Sum of two supplementary angles = 180°

• Larger angle = 112°
• Smaller angle = 68°

$\mapsto 112 \degree + 68 \degree = 180 \degree$

$\mapsto180 \degree = 180 \degree$

Hence Verified !!