ABCD is a trapezium in which AB || DC and ∠A = ∠B = 45º. Find angles C and D of the trapezium.

Solution:

Given, ABCD is a trapezium

AB || DC

∠A = ∠B = 45º

We have to find the angles C and D of the trapezium

We know that opposite angles in a quadrilateral are always supplementary.

So, ∠B + ∠C = 180º

Given, ∠B = 45º

45 + ∠C = 180º

∠C = 180º - 45º

∠C = 135º

Similarly, ∠A + ∠D = 180º

Given, ∠A = 45º

45º + ∠D = 180º

∠D = 180º - 45º

∠D = 135º

Therefore, the angles C and D of trapezium is equal to 135º

✦ Try This: PQRS is a trapezium in which PQ || RS and ∠P = ∠Q = 60º. Find angles C and D of the trapezium.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 8

NCERT Exemplar Class 9 Maths Exercise 8.3 Problem 2

ABCD is a trapezium in which AB || DC and ∠A = ∠B = 45º. Find angles C and D of the trapezium.

Summary:

ABCD is a trapezium in which AB || DC and ∠A = ∠B = 45º. Angles C and D of the trapezium are 135º each

☛ Related Questions:

• The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the para . . . .
• ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus
• E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a par . . . .