Answer: 52°
Step-by-step explanation: In this problem, we're asked to use the diagram shown to find the value of <em>x</em>.
Since the two lines in the figure intersect, we know that they form vertical angles and remember that vertical angles are congruent.
Since our diagram tells us that one angle measures (x + 35)° and the measure of the other angle is (3x + 1)° and we know that these angle measures are equal, we can setup the equation x + 35 = 3x + 1.
Solving from here, we subtract x from both sides to get 35 =2x + 1
and subtracting 1 from both sides we have 34 = 2x.
Now dividing both sides by 2, we find that 17 = x.
Now, we plug a 17 back into one of our angles.
So let's do (x + 35)°
Plugging in a 17, we have (17) + 35 or 52°.
