Answer:
m<1 = 142°
m<3 = 142°
Explanation:
Pre-Solving
We are given two vertical angles, which are <1 and <3.
We know that m<1 = 2x + 26°, and m<3 = 3x - 32°.
We want to find the measure of each angle.
Solving
Solving for x
Recall that vertical angles are congruent by vertical angles theorem.
This means that <1 ≅ <3.
This also means that 2x + 26 = 3x - 32.
We can solve the above equation.
Subtract 2x from both sides.
2x + 26 = 3x - 32.
-2x -2x
_________________
26 = x - 32
Add 32 to both sides.
58 = x
Now, substitute this value of x into the values given.
Values of the angles
Substitute x as 58 in 2x+26 to find the value of <1.
m<1 = 2x + 26 = 2(58) + 26 = 116 + 26 = 142°
We can now substitute x as 58 in 3x - 32 to find the value of <3.
m<3 = 3x - 32 = 3(58) - 32 = 174 - 32 = 142°