Two angles are complementary. Find the measures of both angles if the first angle is 15 degrees smaller than four times the second angle

Question

can you please help me solve this.

Answer 1

Definition: Complimentary angles add up to 90°.

Let angle 1 and 2 be denoted as a1 and a2 respectively. The question states that a1 is 15 degrees (°) smaller than four (4) times a2.

To solve this problem, first write out the algebraic relations or formulas according to the statement and definition as follows:

(1) a1 (°) = (4*a2) - 15 ....or a1 -4a2 = -15

(2) a1 + a2 = 90°

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Now solve the system of equations by eliminating or canceling one of the constants (a1 or a2) to solve for the other constant.

By multiplying equation (2) by 4, you obtain

4a1 + 4a2 = 360°

Then by adding equation (1) and (2) yields

(4a1 + a1) + (4a2 - 4a2) = 360 + (-15).

Then by simplifying, we have the following expression

5a1 + 0a2 = 345 or a1 = 345/5 = 69 degrees.

Therefore, substituting in equation (2) yields

69 + a2 = 90 or a2 = 90 - 69 = 21 degrees

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Check:

(1) a1 = 4a2 -15 --> 69 = 4* 21 -15 = 84 -15 = 69✔

Answer 2

Complementary means they equal 90°

Let's call the smaller angle x

The larger angle is four times the smaller angle minus 15 (4x-15)

So..

X + 4x - 15 = 90

5x = 105

x = 21

Plug in to solve for the larger angle..

4x -15

4(21) - 15 = 69

Check your work..

Does 21 + 69 = 90 ✓

Is 69 four times 21 minus 15 ✓

Answer 3

Complementary means they equal 90°

Let's call the smaller angle x.

So..

90 = x + the larger angle

We know the larger angle is four times the smaller angle minus 15... 4x - 15

So... 90 = x + 4x -15

90 = 5x -15

105 = 5x

21 = x

Now plug in to solve for the larger angle (4x - 15)

4(21) -15 = 69

Check your work...

21+69 = 90 ✓

69 is four times 21 minus 15