Chapter 1.5, Problem 2CYP

To determine

To calculate the complementary angles.

Answer to Problem 2CYP

Smaller angle is 26° and the larger angle is 64°

Explanation of Solution

Given information:

Larger angles is 12 more than twice the measure of the smaller angle.

Formula used:

Sum of two complementary angles is 90°

Calculation:

Let, the smaller angle be “ $x$ ”

Hence, the larger angle is “ $2x+12$ ”

Hence,

  $x+(2x+12)=90$

Opening the brackets,

  $x+2x+12=90$

On solving,

  $3x+12=90$

Shifting the terms,

  $3x=90-12$

On solving,

  $3x=78$

On solving,

  $x=26$

Hence, smaller angle is 26°

For larger angle, substituting the values,

  $2(26)+12$

On solving,

  $64$

Hence, the larger angle is 64°