Question

in a circle angle at one arc is one and half times of the angle at its alternate arc. then what is the measure of Central angle?) *

1 point

a) 72°

b) 108°

c) 90°

d) 144°

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Answer 1

Given : in a circle angle at one arc is one and half times of the angle at its alternate arc

To find : what is the measure of Central angle

Solution:

Sum of angle  at arc and  alternate arc  = 180°

if one angle = x°

then another angle = 3x/2

x + 3x/2  = 180°

=> 5x = 360°

=> x = 72°

measure of Central angle  =  2 ( angle at alternate arc)

=>  measure of Central angle  = 2 * 72°

=> measure of Central angle  = 144°

the measure of Central angle = 144°

option d is correct

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