In the following figure, ABCD and PQRS are parallelograms such that angle D = 120° and angle Q = 70°. Find the value of x.
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Step-by-step explanation:
ABCD is a parallelogram.
=>Opposite angles of parallelogram are congruent.
=>∠DAB = ∠BCD and ∠ABC = ∠ADC = 120°
In ABCD,
∠DAB + ∠BCD + ∠ABC + ∠ADC =360° ( sum of the measure of angles of a quadrilateral)
=>∠BCD+∠BCD +120°+120°=360°
=>2∠BCD =360°-240°
=>2∠BCD =120°
=>∠BCD=60°
PQRS is parallelogram.
=>∠PQR = ∠PSR = 70°
In△CMS,
∠CMS +∠CSM + ∠MCS = 180°
(angle sum property)
=> x + 70° + 60° = 180°
=> x = 50°
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