If the measure of an exterior angle of a triangle is 75 degrees, then what are the measures of the two remote interior angles?
75 degrees. There is an important theorem on this, you ought to know by heart.
To find the measures of the two remote interior angles of a triangle when the measure of an exterior angle is given, follow these steps:
Step 1: Recall that an exterior angle of a triangle is equal to the sum of the two remote interior angles.
Step 2: Let's denote one of the remote interior angles as x.
Step 3: Since the measure of the exterior angle is given as 75 degrees, we can set up an equation:
x + 75 = 180 (Sum of interior angles of a triangle is 180 degrees)
Step 4: Solve the equation for x:
x = 180 - 75
x = 105
Step 5: The other remote interior angle can be found by subtracting the known angle from 180 degrees:
180 - 105 = 75
Therefore, the measures of the two remote interior angles in this triangle are 105 degrees and 75 degrees.