Question

problem 22:
two angles are supplementary. one angle measures 10 more than 9 times the other. find the measures of both angles.

Explanation:

Step1: Set up variables

Let one angle be \(x\). Then the other angle is \(9x + 10\).

Step2: Use the supplementary - angle property

Since supplementary angles sum to \(180^{\circ}\), we have the equation \(x+(9x + 10)=180\).
Simplify the left - hand side: \(x+9x + 10=10x + 10\). So, \(10x+10 = 180\).
Subtract 10 from both sides: \(10x=180 - 10=170\).
Divide both sides by 10: \(x=\frac{170}{10}=17\).

Step3: Find the second angle

Substitute \(x = 17\) into \(9x + 10\). We get \(9\times17+10=153 + 10=163\).

Answer:

The measures of the two angles are \(17^{\circ}\) and \(163^{\circ}\).