Advertisements
Advertisements
प्रश्न
Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.
Advertisements
उत्तर
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
संबंधित प्रश्न
How many diagonals does following have?
A regular hexagon
Complete of the following, so as to make a true statement:
A quadrilateral has ..... vertices, no three of which are .....
Complete of the following, so as to make a true statement:
A point is in the interior of a convex quadrilateral, if it is in the ..... of its two opposite angles.
In Fig. 16.21, the bisectors of ∠A and ∠B meet at a point P. If ∠C = 100° and ∠D = 50°, find the measure of ∠APB.
In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that \[∠COD = \frac{1}{2}(∠A + ∠B) .\]
The measure of angles of a hexagon are x°, (x − 5)°, (x − 5)°, (2x − 5)°, (2x − 5)°, (2x + 20)°. Find the value of x.
Use the information given in the following figure to find :
(i) x
(ii) ∠B and ∠C
Observe the figure below and find out their name.
Measures of the two angles between hour and minute hands of a clock at 9 O’ clock are ______.
In the following figure, What is BD – BE?
