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tankabanditka [31]
3 years ago
10

The sum of the measures of two complementary angles is 90 degrees. If one angle measures 39 degrees more than 2 times the measur

e of its​ complement, find the measures of the two angles.
Mathematics
1 answer:
Digiron [165]3 years ago
5 0

Let 'x' and 'y' be two complementary angles.

The sum of two complementary angles is always 90 degrees.

So, x+y = 90^\circ  

y = 90^\circ - x   (equation 1)

It is given that, one angle measures 39 degrees more than 2 times the measure of its complement.

So, x = 39^\circ+(2 \times y)

x = 39^\circ+2y

Substituting the value of 'y' from equation 1 in the above equation, we get

x = 39^\circ+2(90^\circ-x)

x=39^\circ+180^\circ-2x

x + 2x = 219^\circ

3x = 219^\circ

So, x = 73^\circ

Since, y = 90^\circ-x

y = 90-73 = 17^\circ

Therefore, the measure of two angles are 73^\circ and  17^\circ.

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