Question

In the adjoining figure, angle ADC=130⁰. Find angle ABC​

Answer 1

Answer:

<adc=180

a+d+c=180

a+130+c=180

a+c=180-130

a+c=50

a=25

c=25

<abc=180

ab parallel to dc=165

a=25

c=25

abc=180-50

b=30

Answer 2

• In the adjoining figure, ∠ABC is equal to 50° .

Given :- In the adjoining figure, ∠ADC = 130° .

To Find :-

• ∠ABC .

Concept used :-

• If all four corner of a quadrilateral touches the circumference of the circle, the quadrilateral is known as cyclic quadrilateral .
• Sum of opposite angles of a cyclic quadrilateral is equal to 180° .

Solution :-

from image we can see that,

• All four vertices of quadrilateral ABCD lies at the circumference of the circle .
• Therefore, we can conclude that, ABCD is a cyclic quadrilateral .

So,

→ ∠ADC + ∠ABC = 180° { Opposite angles of a cyclic quadrilateral are supplementry }

putting given value of ∠ADC = 130°,

→ 130° + ∠ABC = 180°

taking 130° to the RHS side and changing the sign,

→ ∠ABC = 180° - 130°

→ ∠ABC = 50° (Ans.)

Hence, ∠ABC is equal to 50° .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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