Question

ABCD is a trapezium in which AB parallel to DC &angle A=angle B=45degree.Find the angles C&D of the trapezium.

Answer 1

Answer:

135° each.

Step-by-step explanation:

Given ABCD is a trapezium with AB || CD and angle A = angle B = 45°.

Since, adjacent angles (angle A and angle B) are equal we can conclude that the trapezium ABCD is isosceles trapezium. Hence, angle C would also be equal to angle D. So let angle C = angle D be x

By angle sum property,

angle A + angle B + angle C + angle D = 360°

→ 45° + 45° + x + x = 360°

→ 2x + 90° = 360°

→ 2x = 360° - 90°

→ 2x = 270°

→ x = 270/2

→ x = 135°

Hence, angle C = angle D = 135°

Answer 2

$\huge{\bold{\underline{\red{\boxed{Answer\::}}}}}$

$\textbf{ABCD is a trapezium and A and B}$ $\textbf{are equal.}$

$\textbf{Also given that AB parallel to CD}$

Means...

$\textbf{C and D are also equal to each other}$. $\textbf{So, let them be x.}$

Now...

$\textbf{\red{Area of trapezium}}$

$\underline{\textbf{Sum of all sides}}$

i.e.

/_A + /_B + /_C + /_D = 360°

45° + 45° + x + x = 360°

90° + 2x = 360°

2x = 360° - 90°

2x = 270°

x = 135°

As...

${angle\:C \:and\: angle\:D\: = \:x}$

So...

${angle\:C \:and \:angle\:D \:= \:135°}$