In the figure, is shown with a ray from passing through point . The measures of several angles are labeled.
Which choice is the value of ?
When you see a triangle with one side extended, focus on the exterior angle. On the SAT, the fastest move is usually to set the exterior angle equal to the sum of the two non-adjacent (remote) interior angles, then solve the one-step equation.
Hints
Identify the exterior angle
Look at the angle labeled . It is outside the triangle and is formed using an extended side.
Connect the exterior angle to the two remote interior angles
For a triangle, an exterior angle equals the sum of the two interior angles that are not adjacent to it.
Write a simple equation
Set equal to , then solve by subtracting.
Desmos Guide
Compute the difference
In Desmos, type 120-45 and press enter.
Interpret the result
Use the value Desmos returns as the measure of .
Step-by-step Explanation
Use the exterior angle relationship
At vertex , the angle is formed by extending a side of the triangle, so it is an exterior angle. An exterior angle equals the sum of the two remote interior angles.
So,
Solve for
Subtract from both sides:
Therefore, the value of is .