Question

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Answer 1

Step-by-step explanation:

Given : ABCD is a quadrilateral

\begin{gathered}\angle A = \angle C...(1) \\\\\angle B = \angle D...(2) \\\\\angle A= 2\angle B ..(3)\end{gathered}

∠A=∠C...(1)

∠B=∠D...(2)

∠A=2∠B..(3)

To find : the measure of each angle

Solution:

we know that sum of all the angles of the quadrilateral is 360 degrees

thus

\angle A +\angle B + \angle C + \angle D = 360^\circ∠A+∠B+∠C+∠D=360

∘

from equation 1 ,2,and 3

2B +B +2B +B = 360

6B = 360

B = 60°

therefore

\begin{gathered}\angle B = \angle C = 60^\circ \\\\\angle A = \angle C = 2\angle B = 2\times 60 = 120^\circ\end{gathered}

∠B=∠C=60

∘

∠A=∠C=2∠B=2×60=120

∘

hence , all the angle are 60°,120°,60°,120°

Answer 2

Answer:

Let angle A be x so angle C is also x

and angle B be y so angle D is also y

now 2y = x

angle B + angle D = y+y = 2y

and 2y = x

so,

angle A + angle B + angle C + angle D = 360 degrees.

x + x + x = 360 degrees

3x = 360 so x = 120

so

angle A = 120, angle B = 60, angle C = 120 and angle D = 60

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