Question

10

65°
A, B, C and D are points on the circumference of the circle.
The line XY is a tangent to the circle at 4.
(a) Find the value of x, giving a reason for your answer.
because
I
(b) Find the value of y, giving a reason for your answer.
because
NOT TO
SCALE
E
(2)
(2)

Answer 1

answer:O A, B, C and D

Explanation:

Answer 2

a. The value of x is 55° because of Alternate segment theorem

b. The value of y is 115° because the sum of the opposite angles of a cyclic quadrilateral is equal to 180°

How to evaluate for the angles in the cyclic quadrilateral quadrilateral

a. The angle between a chord and a tangent is equal to the angle in the alternate segment, this is the angle subtended by the chord in the opposite side of the previous angle. So;

x = 55°

b. The sum of the opposite angles in a cyclic quadrilateral is equal to 180°, so we solve for the angle y as follows:

y + 65° = 180°

y = 180° - 65° {collect like terms}

y = 115°

Therefore, the value of x is 55° because angle between a chord and a tangent is equal to the angle in the alternate segment and the value of y is 115° because the sum of the opposite angles of a cyclic quadrilateral is equal to 180°.