Question

∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left parenthesis, 3, x, minus, 10, right parenthesis, degreesm∠1=(3x−10)
∘
and m, angle, 2, equals, left parenthesis, 8, x, minus, 19, right parenthesis, degreesm∠2=(8x−19)
∘
, then find the measure of angle, 1∠1.

Answer 1

Since angles ∠1 and ∠2 are supplementary, their measures add up to 180 degrees. Thus, we can write the equation:

\[
m∠1 + m∠2 = 180^\circ
\]

Substituting the given expressions for the angles, we have:

\[
(3x - 10) + (8x - 19) = 180
\]

Now, we can combine like terms:

\[
3x + 8x - 10 - 19 = 180
\]

This simplifies to:

\[
11x - 29 = 180
\]

Next, we add 29 to both sides:

\[
11x = 180 + 29
\]
\[
11x = 209
\]

Now, divide both sides by 11:

\[
x = \frac{209}{11}
\]
\[
x = 19
\]

Now that we have the value of \( x \), we can find the measure of angle ∠1:

\[
m∠1 = 3x - 10
\]
\[
m∠1 = 3(19) - 10
\]
\[
m∠1 = 57 - 10
\]
\[
m∠1 = 47^\circ
\]

Therefore, the measure of angle ∠1 is:

\[
\boxed{47^\circ}
\]