For two vertical angles with measures, m<1 =(2x+26) and m<3 = (3x+32)
What is the measure of each angle
Vertical angles are formed when two lines intersect. These angles are congruent, which means they have the same measure.
Thus, we can set up the equation:
m<1 = m<3
2x + 26 = 3x + 32
To solve for x, we can subtract 2x from both sides:
26 = x + 32
Next, we can subtract 32 from both sides:
-6 = x
Now, we substitute this value back into one of the expressions to find the measure of each angle. Let's use m<1:
m<1 = 2x + 26
m<1 = 2(-6) + 26
m<1 = -12 + 26
m<1 = 14
Therefore, the measure of angle 1 (m<1) is 14 degrees. Since vertical angles are congruent, the measure of angle 3 (m<3) is also 14 degrees.