Question

A, B, C and D are points on the circumference of a circle, centre O. Angle ABC = 47°,

a) Work out angle x. Give a reason for your answer.

b) Work out angle y. Give a reason for your answer.

Answer 1

Answer:

x= 23.5°.

y= 94°

Step-by-step explanation:

a) Angle x is an inscribed angle that intercepts arc BC. The measure of an inscribed angle is equal to half the measure of the arc it intercepts. Therefore, angle x = 1/2 * 47° = 23.5°.

b) Angle y is an exterior angle of triangle ABC. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Therefore, angle y = 47° + 47° = 94°.