Advertisements
Advertisements
Question
Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.
Advertisements
Solution
Let ABCD be a quadrilateral.
So, ∠A = ∠C
∠B = ∠D
And ∠A + ∠C = 180°, ∠B + ∠D = 180°
Now, ∠A + ∠A = 180° ...[∠C = ∠A]
⇒ 2∠A = 180°
⇒ ∠A = 90°
Similarly, ∠B = 90°
Hence, each angle is a right angle.
APPEARS IN
RELATED QUESTIONS
In Fig. 16.19, ABCD is a quadrilateral.
Name a pair of adjacent angles.
Complete the following statement by means of one of those given in brackets against each:
If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is ................
Which of the following quadrilateral is not a rhombus?
ABCD is a trapezium in which AB || DC. M and N are the mid-points of AD and the respectively. If AB = 12 cm, MN = 14 cm, then CD =
Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.
In an isosceles trapezium one pair of opposite sides are _____ to each Other and the other pair of opposite sides are _____ to each other.
Two diagonals of an isosceles trapezium are x cm and (3x – 8) cm. Find the value of x.
A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is ______.
Measures of the two angles between hour and minute hands of a clock at 9 O’ clock are ______.
Using the information given, name the right angles in part of figure:
RT ⊥ ST
