Question
For two vertical angles with measures angle 1=(2x+26)° and angle 3=(3x+32)°, what is the measure of each angle?
Answers
GPT 3.5
Vertical angles are angles that share the same vertex and are formed by intersecting lines. When two lines intersect, they form four angles, and the vertical angles are congruent, meaning they have the same measure.
In this case, angle 1 and angle 3 are vertical angles. So, we can set their measures equal to each other:
2x + 26 = 3x + 32
Subtracting 2x from both sides:
26 = x + 32
Subtracting 32 from both sides:
-6 = x
Therefore, the measure of angle 1 is:
2x + 26 = 2(-6) + 26 = 14°
And the measure of angle 3 is:
3x + 32 = 3(-6) + 32 = 14°
So, the measure of each angle is 14°.
In this case, angle 1 and angle 3 are vertical angles. So, we can set their measures equal to each other:
2x + 26 = 3x + 32
Subtracting 2x from both sides:
26 = x + 32
Subtracting 32 from both sides:
-6 = x
Therefore, the measure of angle 1 is:
2x + 26 = 2(-6) + 26 = 14°
And the measure of angle 3 is:
3x + 32 = 3(-6) + 32 = 14°
So, the measure of each angle is 14°.