∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left parenthesis, 4, x, minus, 4, right parenthesis, degrees∠1=(4x−4)

Question

∘
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:

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