Question

If the two angles are complementary, find the measure of each of angle.

Answer 1

D 40 degree and 50 degree

Explanation:

* We can work in units when dealing with tens as 4 + 5 = 9

* As the angle ASD is a Right Angle 4r : 5r = 9r

* 2 angles we see within add up to 90 degree 90 = 9r

ASM + MSO = 90 degree

* 5r = ASM and 4r = MSO = 50 = ASM and 40 = MSO

Therefore ASO - MSO = ASM = 90 - 50 = 40

90 - 50 = 40 and 90 - 5r = 4r

4r = 40 degree and 5r = 50 degree

So just list a few of the above and show that

4r + 5r = 90

9r = 90/9

r = 10

Rounding to zero angles = 40 + 50 = 90 as r = 10

* Answer is D 40 degree and 50 degree

Answer 2

Hi there!

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I believe your answer is:

`\text{D) } 40 \text{ and }50`

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Here’s why:

• Complementary Angles have a sum of 90°.

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`\boxed{\text{Setting up an equation...}}}\\\\ \text{We know that complementary angles add up to 90 degrees.}\\\text{Therefore, the sum of the two angles is 90 degrees.}\\\\\rightarrow 4r + 5r = 90`

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`\boxed{\text{Solving for 'r'...}}\\\\4r + 5r = 90\\---------------\\\rightarrow 9r = 90\\\\\rightarrow (9r=90)/(9)\\\\\boxed{r = 10}`

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`\boxed{\text{Evaluating the expressions given...}}\\\\4r \text{ and } 5r\\----------------\\\boxed{4r}\\\\\rightarrow 4(10)\\\\\rightarrow 4 * 10\\\\\rightarrow\boxed{40}\\----------------\\\boxed{5r}\\\\\rightarrow 5(10)\\\\\rightarrow 5 * 10\\\\\rightarrow \boxed{50}`

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The correct answer should be D.

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Hope this helps you. I apologize if it’s incorrect.