Respuesta :

calculista

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°

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abidemiokin

The measure of <ERK is 55 degrees

Circle geometry

Given the following parameters

arcRK = 70 degrees

Determine the measure of arcEK
arcEK + arcRK + 180 = 360

arcEK + 70 + 180 = 360

arcEK + 250 = 360

arcEK = 110 degrees

<ERK = 1/2 arcEK

<ERK = 1/2(110)
<ERK = 55 degrees

Hence the measure of <ERK is 55 degrees

Learn more on circle geometry here: https://brainly.com/question/24375372

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