ABCD is a quadrilateral such that angle A is equal to Angle B and angle C is equal to angle D if angle A is equal to 2 angle C find the angles of the quadrilateral.
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Answers
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
∘
B=∠C=60
∘
∠A=∠C=2∠B=2×60=120
∘
hence , all the angle are 60°,120°,60°,120°
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