Question

1. ∠uwx is a straight angle. find m∠uwv and m∠xwv.

there is a diagram with a straight line ux, point w in the middle. from w, a vertical line down to v. the angle ∠uwv is labeled (x + 20)°, and ∠xwv is labeled x°

Explanation:

Step1: Determine the sum of angles

Since $\angle UWX$ is a straight angle, it measures $180^\circ$. The angles $\angle UWV$ and $\angle XWV$ are adjacent and form $\angle UWX$, so $(x + 20)^\circ + x^\circ = 180^\circ$.

Step2: Solve for x

Combine like terms: $2x + 20 = 180$. Subtract 20 from both sides: $2x = 160$. Divide by 2: $x = 80$.

Step3: Find $m\angle UWV$

Substitute $x = 80$ into $(x + 20)^\circ$: $80 + 20 = 100^\circ$.

Step4: Find $m\angle XWV$

Substitute $x = 80$ into $x^\circ$: $80^\circ$.

Answer:

$m\angle UWV = 100^\circ$, $m\angle XWV = 80^\circ$