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olganol [36]
2 years ago
9

Find the measures of the complementary angles that satisfy each case.

Mathematics
1 answer:
djverab [1.8K]2 years ago
5 0

Given:

The measure of the first angle is 40° less than the measure of the second.

To find:

The measures of the complementary angles that satisfy the given condition.

Solution:

Let the measure of first angle be x°.

According to the given condition,

First angle = Second angle - 40°

x^\circ =\text{Second angle}-40^\circ

Add 40° on both sides.

(x+40)^\circ =\text{Second angle}

We know that, sum of complementary angles is 90°. So,

First angle + Second angle = 90°

x^\circ +(x+40)^\circ =90^\circ

2x^\circ +40^\circ =90^\circ

2x^\circ =90^\circ -40^\circ

2x^\circ =50^\circ

Divide both sides by 2.

x^\circ =25^\circ

So, the measure of first angle is 25°.

(x+40)^\circ =(25+40)^\circ =65^\circ

So, the measure of second angle is 65°.

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