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

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Answer 1 · 2016-01-06T16:01:31

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

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#