Question

find the value of mentioned angle S is the given circle with centre O​

Answer 1

Step-by-step explanation:

Given that: OA = OC = R

OCA = 48°

since angle OCA = 48°

OA = OC. (Given )

OAC = OCA ( angles opposite to equal sides of a triangle )

OAC = 48°

AOC + OCA + OAC = 180 Degree ( triangle sum property )

AOC = 180 - ( OCA + OAC )

AOC = 180 - ( 48 + 48 )

AOC = 180 - 96

AOC = 84°

since

2 ADC = AOC ( angle subtended by the same arc at the centre is twice angle subtended by the arc at any point on the remaining arc )

ADC = AOC /2

ADC = 84 / 2

ADC = 42°

now, angle subtended by arc ADC at the centre = 360 - 84 = 276°

2 ABC = reflex of AOC

ABC = 276 / 2

ABC = 138°

hence, angle x = ADC = 42°

angle y = ABC = 138°

hope it will help you

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