The sum of the measures of two vertical angles is 300° . Solve for the measure of each angle.(1 point)
Responses
75°
75 degrees
150°
150 degrees
120°
120 degrees
90°
90 degrees
75°
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
14
98
18
72
18
For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?(1 point)
Responses
15.3°15.3 degrees
29°29 degrees
6°6 degrees
53°
Angles 2 and 4 are vertical angles, so they are congruent:
m∠2 = m∠4
5x + 23 = 3x + 35
2x = 12
x = 6
Now, plug in x = 6 to find the measures of the angles:
m∠2 = 5(6) + 23 = 30 + 23 = 53°
m∠4 = 3(6) + 35 = 18 + 35 = 53°
So, the measure of each angle is 53 degrees.