In a geometric figure two intersecting lines creating four angles. If and are a vertical pair,

Question

, and , what is the value of ? (1 point)
∠1 ∠3
m∠1 = (4x + 26) ° m∠3 = 98° x
72
14
98
18

Answer 1

Since ∠1 and ∠3 are a vertical pair, they are equal in measure.

Given m∠1 = (4x + 26) ° and m∠3 = 98°, we can equate the two expressions:

(4x + 26) ° = 98°

Now, solve for x:

4x + 26 = 98

Subtract 26 from both sides:

4x = 72

Divide both sides by 4:

x = 18

Therefore, the value of x is 18.

Now, substitute this value of x into the expression for ∠1 to find its measure:

m∠1 = (4x + 26) °
m∠1 = (4(18) + 26) °
m∠1 = (72 + 26) °
m∠1 = 98 °

So, the value of ∠1 is 98°.

Option: 98.