Question

problem 21: (first taught in lesson 16) the difference between the measures of two supplementary angles is 42. find both angles. after you enter your answer press go.

Explanation:

Step1: Set up equations

Let the two supplementary angles be $x$ and $y$ ($x>y$). Supplementary - angle property gives $x + y=180$, and the given condition gives $x - y = 42$.

Step2: Solve the system

Add the two equations: $(x + y)+(x - y)=180 + 42$. Simplify to get $2x=222$, so $x = 111$.

Step3: Find the other angle

Substitute $x = 111$ into $x + y=180$. Then $111+y=180$, and $y=180 - 111=69$.

Answer:

69, 111