Question

what are the numerical measures of each angle in the diagram? ∠1 and ∠3 measure degrees. ∠2 and ∠4 measure degrees. (3x - 1)° (2x + 9)°

Explanation:

Step1: Set up equation

Vertical - angles are equal. So, $3x - 1=2x + 9$.

Step2: Solve for x

Subtract $2x$ from both sides: $3x-2x-1=2x - 2x+9$, which gives $x - 1=9$. Then add 1 to both sides: $x=9 + 1=10$.

Step3: Find measure of ∠1 and ∠3

Substitute $x = 10$ into the expression for ∠1 (and ∠3 since they are equal). $3x-1=3\times10 - 1=29$ degrees.

Step4: Find measure of ∠2 and ∠4

Since ∠1 and ∠2 are supplementary (a straight - line is 180 degrees), ∠2=180 - ∠1. ∠2=180 - 29 = 151 degrees. And ∠4 has the same measure as ∠2, so ∠4 = 151 degrees.

Answer:

∠1 and ∠3 measure 29 degrees.
∠2 and ∠4 measure 151 degrees.