Question

Given: circle k(O), m RK =70° Find: m∠ERK

Answer 1

Answer:

The measure of angle ERK is 55°

Step-by-step explanation:

step 1

Find the measure of arc EK

we know that

The diameter divide the circle into two equal parts

In this problem

EOR is a diameter

see the attached figure to better understand the problem

so

arc EK + arc RK=180°

substitute the given values

arc EK + 70°=180°

arc EK=180°-70°=110°

step 2

Find the measure of angle ERK

we know that

The inscribed angle is half that of the arc it comprises.

m∠ERK=(1/2)[arc EK]

substitute  

m∠ERK=(1/2)[110°]=55°