Answer:
Step-by-step explanation:
90 = (90-x)-x + 74
16 = 90-2x
2x = 74
x = 37 (angle)
90-x = 53 (complement)
The measure of the two angles which are complementary angles to each other is 37 degrees and 53 degrees.
The two angles are called complementary angles, when the sum of these two angle is equal to the 90 degrees.
Suppose there are two angles, angle A and angle B. These two angles will be complementary if,
[tex]m\angle A+m\angle B =90^o[/tex]
Here, the sum of the measures of two complementary angles is 74° greater than the difference of their measures.
Suppose the two angle are ∠A and ∠B. As these angles are complementary. Therefore, the sum of these angles will be,
[tex]m\angle A+m\angle B =90^o[/tex] ....1
Now, this sum is 74 degrees greater than the difference of their measures. Therefore,
[tex]m\angle A-m\angle B =90-74\\m\angle A-m\angle B =16\\m\angle A =16+m\angle B[/tex]
Put the value of angle A in the equation 1 as,
[tex](16+m\angle B )+m\angle B =90^o\\2m\angle B =90-16\\m\angle B =\dfrac{74}{2}\\m\angle B =37^o[/tex]
Put this value in the equation 1 as,
[tex]m\angle A+37=90^o\\m\angle A=90-37\\m\angle A=53^o[/tex]
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Hence, the measure of the two angles which are complementary angles to each other is 37 degrees and 53 degrees.
Learn more about the complementary angles here;
https://brainly.com/question/16281260
