Question

in a parallelogram ABCD if angle A= (3x-20)° , angle B=(y+15)° , angle C=(X+40)° then find the values of X and Y ​

Answer 1

3x-20=x+40

2x=60

x=30°

(3x-20)+(y+15)=180°

y=95°

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Answer 2

Step-by-step explanation:

Given : In a parallelogram ABCD, if ∠A = (3x - 20)°, ∠B = (y + 15)° and ∠C = (x + 40)°.

 

We have , parallelogram ABCD,

In parallelogram Opposite Angles are equal

∴ ∠ A = ∠ C

⇒ (3x - 20)° = (x + 40)°

⇒ 3x - x = 40° + 20°

⇒ 2x = 60°

⇒ x = 60°/2

⇒ x = 30° …………(1)

 

Since, Sum of Consecutive interior angles are supplementary, Then  

∠A + ∠B = 180°

⇒ 3x – 20° + y + 15 = 180°

⇒ 3x + y = 180° +  20° - 15°

⇒ 3x + y = 180° + 5°

⇒ 3x + y = 185°

⇒ 3 × 30° + y = 185°

[From eq 1]

⇒ 90° + y = 185°

⇒ y = 185° – 90°  

⇒ y = 95°

Hence , the values of x is 30° and y is 95°