Advertisements
Advertisements
Question
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = x° and ∠D = (3x – 20)°; find the value of x.
Advertisements
Solution
∵ AB || DC and BC is transversal
∴ ∠A and ∠B are Co-interior angles with their sum = 180°
i.e. ∠A + ∠D = 180°
⇒ x° + (3x – 20)° = 180°
⇒ x° + 3x° – 20° = 180°
⇒ 4x° = 180° + 20°
x° = `200/4` = 50°
∴ Value of x = 50°
APPEARS IN
RELATED QUESTIONS
Complete of the following, so as to make a true statement:
The number of pairs of adjacent angles of a quadrilateral is .......
Two angles of a quadrilateral are of measure 65° and the other two angles are equal. What is the measure of each of these two angles?
The four angles of a quadrilateral are as 3 : 5 : 7 : 9. Find the angles.
The sides of a quadrilateral are produced in order. What is the sum of the four exterior angles?
In a convex hexagon, prove that the sum of all interior angle is equal to twice the sum of its exterior angles formed by producing the sides in the same order.
In the given figure, PQRS is an isosceles trapezium. Find x and y.
The following figure shows a quadrilateral in which sides AB and DC are parallel. If ∠A : ∠D = 4 : 5, ∠B = (3x – 15)° and ∠C = (4x + 20)°, find each angle of the quadrilateral ABCD.
Using the information given, name the right angles in part of figure:
AC ⊥ BD
What conclusion can be drawn from part of given figure, if DC is the bisector of ∠ADB, CA ⊥ DA and CB ⊥ DB?
Can we have two obtuse angles whose sum is a reflex angle? Why or why not?
