Question

Given that AB and CD are the two parallel sides of
the trapezium ABCD, find x, y, and z.
​

Answer 1

Given

• AB ll CD

To find

value of x, y & z

Concept used

Here the concept of parallel lines, corresponding angles, adjacent angles and angle sum property is used.

• corresponding angles are equal.

• sum of angles in an trapezium is 360°
• sum of adjacent angles is 180°

Solution

$\sf{ \implies \angle \: x = \angle \: EDC \: (corresponding \: angles)} \\ \sf{ \implies \angle \: x = 100 \degree}$

$\sf {\implies\angle y= 180° -100° ( Adjacent \: angles )} \\ \sf{ \implies \: angle \: y =80 \degree}$

$\sf{\implies \angle y + \angle x+ \angle z +65° = 360° ( angle \: sum \: property)} \\ \\ \sf{ \implies \: 100 + 80 + 65 + \angle \: z = 360 \degree} \\ \\ \sf{ \implies\angle \: z = 115 \degree}$

____________________

Answer 2

Answer:

Given

AB ll CD

To find

value of x, y & z

Concept used

Here the concept of parallel lines, corresponding angles, adjacent angles and angle sum property is used.

corresponding angles are equal.

sum of angles in an trapezium is 360°

sum of adjacent angles is 180°

Solution

⟹∠x=∠EDC(correspondingangles)

⟹∠x=100°

⟹∠y=180°−100°(Adjacentangles)

⟹angley=80°

⟹∠y+∠x+∠z+65°=360°(angle sum property)

⟹100+80+65+∠z=360°

⟹∠z=115°

____________________