Question

Part A: find the measure of x and y

Part B: choose the correct degree measure for arc JKL

Answer 1

x = 7

y = 4

Arc JKL = 262°

Explanation:

Find the diagram attached

Using the theorem;

Sum of opposite angle of the quadrilateral is 180°

7x+131 = 180

7x = 180-131

7x = 49°

x = 49/7

x = 7

Similarly;

11x+y+99 = 180°

11(7)+y+99 = 180°

77+99+y = 180

176+y = 180

y = 180-176

y = 4

arc JKL is the obtuse angle at the centre

Arc JKL = 360-(angle at the centre)

Angle at the centre is twice angle at the circumference.

Angle at the centre = 2(7x)

Angle at the centre = 2(49)

Angle at the centre = 98°

Arc JKL = 360-98

Arc JKL = 262°