Question

In a geometric figure two intersecting lines creating four angles. If ∠1 and ∠3 are a vertical pair, m∠1=(4x+26)° , and m∠3=98° , what is the value of x ?(1 point)Responses

Answer 1

[AI-generated answer — Bot GPT-4o]

Vertical angles are always congruent, which means they have the same measure.

Given:
\( \text{m}\angle 1 = (4x + 26)^\circ \)
\( \text{m}\angle 3 = 98^\circ \)

Since \( \angle 1 \) and \( \angle 3 \) are vertical angles, we have:

\[ 4x + 26 = 98 \]

To solve for \( x \), we will isolate \( x \):

1. Subtract 26 from both sides:
\[ 4x + 26 - 26 = 98 - 26 \]
\[ 4x = 72 \]

2. Divide both sides by 4:
\[ \frac{4x}{4} = \frac{72}{4} \]
\[ x = 18 \]

So, the value of \( x \) is \( 18 \).