Question

Find the measures of the angles.

Answer 1

Both angles are complementary

`\\ \sf\bull\dashrightarrow x+51+2x=90`

`\\ \sf\bull\dashrightarrow 2x+x+51=90`

`\\ \sf\bull\dashrightarrow 3x+51=90`

`\\ \sf\bull\dashrightarrow 3x=90-51=39`

`\\ \sf\bull\dashrightarrow x=(39)/(3)`

`\\ \sf\bull\dashrightarrow x=13`

• m<1=13+51=64
• m<2=2(13)=26

Answer 2

m < 1 = 64°

m < 2 = 26°

Explanation:

Given that m < 1 and m < 2 are complementary angles whose sum add up to 90°, and that:

m < 1 = (x + 51)° and m < 2 = 2x°,

We can write the following equation to solve for the measurements of angles 1 and 2:

m < 1 + m < 2 = 90°

Substitute m < 1 and m < 2 into the equation:

(x + 51)° + 2x° = 90°

3x° + 51° = 90°

Subtract 51° on both sides of the equation:

3x° + 51° - 51° = 90° - 51°

3x° = 39°

Divide both sides by 3:

`(3x)/(3) = (39)/(3)`

x = 13°

Substite x = 13° into m < 1 and m < 2 to find their measurements:

m < 1 = (x + 51)° = 13° + 51° = 64°

m < 2 = 2x° = 2(13)° = 26°

To check the validity of the answers, we can substitute m < 1 = 64° and m < 2 = 26° into the original equation to see if their measurements add up to 90°:

m < 1 + m < 2 = 90°

64° + 26° = 90°

Therefore, the derived answers are correct.