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 ?

Question

responses:
72
14
18
98

Answer 1

To solve this problem, we can use the property that vertical angles are congruent. This means that ∠1 and ∠3 are equal in measure.

Given that m∠1 = (4x + 26)° and m∠3 = 98°, we can set up the equation:
4x + 26 = 98

To isolate x, we will subtract 26 from both sides of the equation:
4x = 98 - 26
4x = 72

Finally, divide both sides by 4 to solve for x:
x = 72/4
x = 18

Therefore, the value of x is 18.