Question

what is the measure of y in the figure below?
a 40
b 50
c 60
d 90

Explanation:

Step1: Recall the sum of angles around a point

The sum of angles around a point is \(360^{\circ}\).

Step2: Set up the equation

We have \(y + 50+90 + 40+y= 180\) (since we consider a straight - line pair of angles. Another way: sum of angles around a point is \(360^{\circ}\), but if we consider the angles on one side of a straight line (semicircle), the sum is \(180^{\circ}\)). The angles \(50^{\circ}\), \(90^{\circ}\), \(40^{\circ}\) and \(y^{\circ}\) lie on a straight line. So, \(y+50 + 90+40=180\).

Step3: Solve the equation

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Answer:

C. \(60\)