Question

An angle measures 4° less than the measure of its complementary angle. What is the measure of each angle?

Answer 1

Step-by-step explanation:

L=larger angle; S=smaller angle=L-4

L+S=90 degrees Substitute for S

L+L-4=90 degrees Add 4 to each side

L+L=94 degrees

2L=94 degrees Divide each side by 2.

L=47 degrees ANSWER 1: The larger angle is 47 degrees

S=L-4=47-4=43 degrees ANSWER 2: The smaller angle is 43 degrees.

CHECK:

L+S=90 degrees

47 degrees + 43 degrees=90 degrees

Answer 2

Answer: The measure of larger angle is 47° and the measure of smaller angle is  43°.

Step-by-step explanation:

Let the larger angle be x° and the smaller angle be (x - 4)°

Now, the sum of angles since it is complementary = 90°

we can write x° + (x - 4)°= 90°

⇒ x° + (x - 4)°= 90°

⇒ 2x°- 4° = 90°

⇒ 2x° = 94°

⇒ x° =47°

Now, smaller angle = 47° - 4° = 43°

Hence, the measure of larger angle is 47° and the measure of smaller angle is  43°.

verification:

larger angle + smaller angle = 90°

47° + 43°

= 90°

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