Question

Find the measures of the supplementary angles if their measures are in ratio of 2:3

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Answer 1

The measures are 72 degrees and 108 degrees.

Explanation:

Supplementary angles means that the two angles add up to 180 degrees. So if we let the smallest angle equal x, we can say

x+(3/2)x=180

or

5/2x=180

Multiplying both sides by 2/5, we find

x=180*2/5=72

Thus, the smallest angle is 72 degrees. Now we subtract 72 from 180 to get 108. Checking our work, we see that 72:108=2:3. So, the measures are 72 degrees and 108 degrees.

Answer 2

Two supplementary angles are 72° and 108° .

Explanation:

we have given the measure of ratio of two angles is 2:3.

Let the two angles be 2x and 3x.

We know the sum of supplementary angle is 180°

Therefore,

2x + 3x = 180°

or 5x = 180°

or x = 180°/5

or x =36°

Hence, the first angle = 2x =2×36 = 72°

And Second angle = 3x = 3×36 = 108°