In a geometric figure two intersecting lines creating four angles. If and are a vertical pair,
, and , what is the value of ? (1 point)
∠1 ∠3
m∠1 = (4x + 26) ° m∠3 = 98° x
72
14
98
18
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.