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°
[tex]x^\circ =\text{Second angle}-40^\circ [/tex]
Add 40° on both sides.
[tex](x+40)^\circ =\text{Second angle}[/tex]
We know that, sum of complementary angles is 90°. So,
First angle + Second angle = 90°
[tex]x^\circ +(x+40)^\circ =90^\circ [/tex]
[tex]2x^\circ +40^\circ =90^\circ [/tex]
[tex]2x^\circ =90^\circ -40^\circ [/tex]
[tex]2x^\circ =50^\circ [/tex]
Divide both sides by 2.
[tex]x^\circ =25^\circ [/tex]
So, the measure of first angle is 25°.
[tex](x+40)^\circ =(25+40)^\circ =65^\circ[/tex]
So, the measure of second angle is 65°.
