Question

if the sum of angles of a triangle is X and the sum of the angles of a quadrilateral is y, then A. X=2Y B. X=Y C. 2X=Y D. X+Y=360°
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Answer 1

Answer:

Let ABCD be a cyclic quadrilateral.

∠A=2x+4,∠B=y+3,∠C=2y+10,∠D=4x−5

In cyclic quadrilateral the sum of the opposite angles in 180°. Therefore,

∠A+∠C=180°

⇒2x+4+2y+10=180°

⇒2x+2y=166°

⇒x+y=83°→1

∠B+∠D=180°

⇒y+3+4x−5=180°

⇒4x+y=182°→2

Solving 1 and 2, we get

4x+y−x−y=182°−83°⇒3x=99°⇒x=33°

& 33°+y=83°⇒y=83°−33°=50°

∴∠A=2×33°+4=70°,∠B=50°+3=53°

∠C=2×50°+10=110°,∠D=4×33°−5=127°

solution

Answer 2

Option C is correct answer

2X = Y

Step-by-step explanation:

sum of angles of a triangle = 180°

Sum of the angles of a quadrilateral = 360°

option C

2X = Y

2(180) = 360°

360° = 360°

RHS is equal to LHS

If we take option A

X = 2Y

180° = 2(360)

180° = 720°

RHS is not equal to LHS

If we take option B

X=Y

180° = 360

RHS is not equal to LHS

If we take option D

X + Y = 360°

180 + 360 = 360

540 = 360

RHS is not equal to LHS

Hope it will help you

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