Question

∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left parenthesis, 3, x, minus, 28, right parenthesis, degreesm∠1=(3x−28)
∘
and m, angle, 2, equals, left parenthesis, x, minus, 4, right parenthesis, degreesm∠2=(x−4)
∘
, then find the measure of angle, 1∠1.

Answer 1

Two angles are supplementary if the sum of their measures is \(180^\circ\). Given:

- \( m\angle 1 = 3x - 28 \)
- \( m\angle 2 = x - 4 \)

We can set up the equation for supplementary angles:

\[
m\angle 1 + m\angle 2 = 180^\circ
\]

Substituting the values of \( m\angle 1 \) and \( m\angle 2 \):

\[
(3x - 28) + (x - 4) = 180
\]

Now, combine like terms:

\[
3x + x - 28 - 4 = 180
\]

This simplifies to:

\[
4x - 32 = 180
\]

Next, add 32 to both sides:

\[
4x = 212
\]

Now, divide by 4:

\[
x = 53
\]

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

\[
m\angle 1 = 3x - 28
\]

Substitute \( x = 53 \):

\[
m\angle 1 = 3(53) - 28
\]

Calculating inside the parentheses:

\[
m\angle 1 = 159 - 28
\]
\[
m\angle 1 = 131
\]

Thus, the measure of angle 1 is \( \boxed{131} \) degrees.