Question

ABCD is a trapezium such that AB parallel to DC find angle D and angle C and verify that sum of the four angles is 360 °

Answer 1

Answer:

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Answer 2

The measure of  angle C  and D is 110° and 140°

Step-by-step explanation:

given : ABCD is a trapezium such that AB parallel to DC

solution :

since ,

AB ║ CD

and AD and BC are the transversal line

then

$\angle B + \angle C = 180^\circ \\70 + \angle C = 180 \\ \angle C = 180 - 70\\ \angle C = 110^\circ$

similarly

$\angle A + \angle D= 180^\circ \\40 + \angle D = 180 \\ \angle D = 180 - 40\\ \angle D = 140^\circ.$

using (sum of the angle on the same side of the transversal )

hence ,

$\angle C = 110^\circ \\\\\angle D = 140^\circ$

now ,trapezium is a quadrilateral

therefore ,

$\angle A + \angle B + \angle C + \angle D = 360^\circ \\\\40 + 70 + 110 + 140 = 360^\circ\\\\360^\circ =360^\circ$

hence proved

#Learn more :

ABCD is a trapezium such that AB||DC. Find ∠D and ∠C and verify that sum of the four angles is 360degree.

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