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Semenov [28]
2 years ago
12

An angle measures 15 degrees more than its complement. Find the measures of the two angles

Mathematics
2 answers:
kap26 [50]2 years ago
5 0

Answer:

The first angle is 37.5° and the second would be 52.5°

Step-by-step explanation:

Angles are complementary when their sums add up to 90°.

x+(x+15) = 90\\x+x+15=90\\x+x=75\\x=37.5

The first angle is 37.5° and the second would be 52.5°, after we plug in x.

<em>Have a nice day. Feel free to ask questions. Spread The Love.</em>

kakasveta [241]2 years ago
4 0

Answer:

  • Angle 1 = x = 37.5°
  • Angle 2 = x + 15 = 52.5°

Concept:

Here, we need to know the idea of the complementary angle.

Two angles are said to be complementary if they add up to 90 degrees.

Be aware that three or more angles cannot be complementary even if their sum is 90 degrees.

Solve:

<u>Given information</u>

Angle 1 = x

Angle 2 = x + 15

<u>Given expression deducted from the definition of the complementary angle</u>

Angle 1 + Angle 2 = 90

<u>Substitute values into the expression</u>

(x) + (x + 15) = 90

<u>Combine like terms</u>

(x + x) + 15 = 90

2x + 15 = 90

<u>Subtract 15 on both sides</u>

2x + 15 - 15 = 90 - 15

2x = 75

<u>Divide 2 on both sides</u>

2x / x = 75 / 2

\boxed{x=37.5}

<u>Find the measure of angle 2</u>

Angle 2 = x + 15 ⇔ <em>Given expression</em>

Angle 2 = (37.5) + 15 ⇔ <em>Substitute values into the expression</em>

Angle 2 = \boxed{52.5} ⇔ <em>Simplify by addition</em>

Hope this helps!! :)

Please let me know if you have any questions

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