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
\[∠A + ∠B + ∠C +∠D = 360° \]
\[ \Rightarrow ∠A +∠B + 100°+ 50° = 360° \]
\[ \Rightarrow ∠A + ∠B = 210° . . . (i)\]
\[\text{ In } \bigtriangleup APB, \text{ we have } : \]
\[\frac{1}{2}∠A + \frac{1}{2}∠B + ∠APB = 180° \]
\[ \Rightarrow ∠APB = 180° - \frac{1}{2}\left( ∠A + ∠B \right)\]
\[\text{ From (i), we get: } \]
\[ \Rightarrow ∠APB = 180° - \left( \frac{1}{2} \times 210° \right) \]
\[ \therefore ∠APB = 75° \]
APPEARS IN
संबंधित प्रश्न
Complete of the following, so as to make a true statement:
A quadrilateral has ....... sides.
Complete of the following, so as to make a true statement:
A diagonal of a quadrilateral is a line segment that joins two ...... vertices of the quadrilateral.
A quadrilateral has three acute angles each measures 80°. What is the measure of the fourth angle?
Three angles of a quadrilateral are equal. Fourth angle is of measure 150°. What is the measure of equal angles.
Which of the following quadrilateral is not a rhombus?
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.
Find the angles of a pentagon which are in the ratio 4: 4: 6: 7: 6.
ABCDE is a pentagon in which AB is parallel to DC and ∠A : ∠E : ∠D = 1 : 2 : 3. Find angle A.
Which of the following is a key requirement for correctly naming a □ABCD?
