Question

If ∠1 and ∠2 are supplementary angles, and m∠1 = (3x - 10)° and m∠2 = (8x - 19)°, then find the measure of ∠1.

Answer 1

To find the measure of angle ∠1, set up an equation using the fact that ∠1 and ∠2 are supplementary angles. Solve for x and substitute it back into the equation for ∠1 to find its measure.

Step-by-step explanation:

To find the measure of angle ∠1, we can set up an equation using the fact that ∠1 and ∠2 are supplementary angles. Supplementary angles add up to 180 degrees, so we have:

(3x - 10) + (8x - 19) = 180

Combine like terms:

11x - 29 = 180

Add 29 to both sides:

11x = 209

Divide both sides by 11:

x = 19

Substitute the value of x back into the equation for ∠1:

∠1 = (3(19) - 10)

∠1 = 47