Question

∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left parenthesis, 4, x, minus, 4, right parenthesis, degrees∠1=(4x−4)
∘
and mangle, 2, equals, left parenthesis, 5, x, minus, 29, right parenthesis, degrees∠2=(5x−29)
∘
, then find the measure of angle, 1∠1.

Answer 1

Since \(\angle 1\) and \(\angle 2\) are vertical angles, they are equal. This gives us the equation:

\[
\angle 1 = \angle 2
\]

Substituting the expressions provided for \(\angle 1\) and \(\angle 2\), we have:

\[
4x - 4 = 5x - 29
\]

Now, let's solve for \(x\).

1. First, subtract \(4x\) from both sides:

\[
-4 = 5x - 4x - 29
\]

This simplifies to:

\[
-4 = x - 29
\]

2. Next, add \(29\) to both sides:

\[
-4 + 29 = x
\]

This simplifies to:

\[
x = 25
\]

Now that we found \(x\), we can substitute this value back into the expression for \(\angle 1\) to find its measure:

\[
\angle 1 = 4x - 4
\]

Substituting \(x = 25\):

\[
\angle 1 = 4(25) - 4
\]

Calculating this gives:

\[
\angle 1 = 100 - 4 = 96
\]

Thus, the measure of \(\angle 1\) is:

\[
\boxed{96} \text{ degrees}
\]