Question

1 ptsQuestion 3Two angles are complementary. The smaller angle is 42 degrees less than the largerangle. What is the measurement of the smaller angle?Be precise in the measurement, including any decimal value. You only need toenter the value for the angle. No other symbols or unit information needed.

Answer 1

It is given that two angles are complementary.

Let x be the larger angle.

It is given that The smaller angle is 42 degrees less than the larger angle

`\text{The smaller angle=}x-42^o`

We know that the sum of the complementary angles is 90 degrees.

`\text{the larger angle+ the smaller angle =}90^o`

Substitute the larger angle =x and the smaller angle =x-42, we get

`x+x-42^o=90^o`

`2x-42^o=90^o`

Transferring 42 to the right-hand side, we get

`2x=90^o+42^o`

`2x=132^o`

`x=(132^o)/(2)`

`x=66^o`
`T\text{he larger angle=x=}66^o`
`\text{The smaller angle =}x-42^o=66^o-42^o=24^o`

Hence the given two complementary angles are

`66^o,24^o`