Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
\[∠A + ∠B + ∠C +∠D = 360° \]
\[ \Rightarrow ∠A +∠B + 100°+ 50° = 360° \]
\[ \Rightarrow ∠A + ∠B = 210° . . . (i)\]
\[\text{ In } \bigtriangleup APB, \text{ we have } : \]
\[\frac{1}{2}∠A + \frac{1}{2}∠B + ∠APB = 180° \]
\[ \Rightarrow ∠APB = 180° - \frac{1}{2}\left( ∠A + ∠B \right)\]
\[\text{ From (i), we get: } \]
\[ \Rightarrow ∠APB = 180° - \left( \frac{1}{2} \times 210° \right) \]
\[ \therefore ∠APB = 75° \]
संबंधित प्रश्न
Complete of the following, so as to make a true statement:
A quadrilateral has ..... vertices, no three of which are .....
The angles of a quadrilateral are 110°, 72°, 55° and x°. Find the value of x.
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?
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.
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 =
Write, giving reason, the name of the figure drawn alongside. Under what condition will this figure be a square.
Observe the figure below and find out their name.
A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is ______.
In quadrilateral HOPE, the pairs of opposite sides are ______.
In the following figure, What is AE + EC?
