Question

Supplementary angles are in the ratio of 3 to 2. What is the measure of the larger angle?

Answer 1

The larger of the two supplementary angles is `=color(blue)( 108^o`

Explanation:

The supplementary angles are in the ratio `3:2`,
so let us depict the angles as `3x^o, 2x^o`

As per property , when two angles are supplementary they add up to `180^o` :

`color(green)(3x^o + 2x^o =180^o`

`5x^o =180^o`

`x^o=36^o`,

Angle `1 = 3x^o = 3 xx36^o = 108^o`
Angle `2 = 2x^o = 2 xx 36^o = 72^o`