Question

in a linear - angle pair, the measure of the larger angle is 15 degrees less than twice the measure of the smaller angle. find the measures of both angles. show the work that leads to your answers.

Explanation:

Step1: Define variables

Let the measure of the smaller angle be $x$ degrees. Then the measure of the larger angle is $2x - 15$ degrees.

Step2: Use the linear - angle - pair property

Since the two angles form a linear - angle pair, their sum is 180 degrees. So, $x+(2x - 15)=180$.

Step3: Simplify the equation

Combine like terms: $x + 2x-15=180$, which gives $3x-15 = 180$.

Step4: Solve for $x$

Add 15 to both sides of the equation: $3x-15 + 15=180 + 15$, so $3x=195$. Then divide both sides by 3: $x=\frac{195}{3}=65$.

Step5: Find the measure of the larger angle

Substitute $x = 65$ into the expression for the larger angle: $2x-15=2\times65-15=130 - 15 = 115$.

Answer:

The smaller angle is 65 degrees and the larger angle is 115 degrees.