To find the measures of the two vertical angles (angle 1 and angle 3), we need to set them equal to each other and solve for x.
According to the Vertical Angle Theorem, vertical angles are congruent, which means they have the same measure.
So, we can write the equation:
3x+15 = x+45
First, let's isolate the variable by subtracting x from both sides:
2x + 15 = 45
Next, let's isolate the variable further by subtracting 15 from both sides:
2x = 30
Finally, let's solve for x by dividing both sides by 2:
x = 15
Now that we have the value of x, we can substitute it back into the expressions for angle 1 and angle 3 to find their measures:
angle 1 = 3x + 15 = 3(15) + 15 = 45 + 15 = 60°
angle 3 = x + 45 = 15 + 45 = 60°
Therefore, the measure of each angle is 60°.
For two vertical angles with measures angle1=(3x+15)° and angle3=(x+45)°, what is the measure of each angle?
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