quadrilateral ABCD is cyclic, angle A=4x°, angleC=(3x+5)°, find angle C
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Given:
- ABCD is a cyclic quadrilateral.
- Angle A = 4x⁰
- Angle C = (3x-5)⁰
To find:
- Angle C
Solution:
We know that ABCD is a cyclic quadrilateral.
/_A+/_C = 180⁰ [Opposite side of quadrilateral]
4x⁰+(3x+5)⁰ = 180⁰
4x⁰+3x⁰+5⁰ =180⁰
7x⁰= 180⁰-5⁰
7x⁰= 175⁰
x = 175/7
x = 25⁰
_______________
So, the Value of /_A = 4x⁰ = 4(25)⁰= 100⁰
The value of /_C = 3x-5⁰ = 3(25)⁰+5⁰ = 80⁰
Verification:
- Sum of opposite angle in cyclic quadrilateral = 180⁰
/_A+/_C = 180⁰
100⁰+80⁰ = 180⁰
- Hence, proved.
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