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| 1. |
In a parallelogram ABCD, if a. angle A=(2x+20)^; angle B=(3x-30)^ , find the value of x^ prime b. angle A=3y, angle B=2y+30^ find the value f^ prime prime y^ prime |
| Answer» LET ABCD be a CYCLIC quadrilateral.∠A=2x+4,∠B=y+3,∠C=2y+10,∠D=4x−5In 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°→2Solving 1 and 2, we get4x+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° | |