Advertisements
Advertisements
प्रश्न
The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sided of the polygon.
Advertisements
उत्तर
\[\left\{ \left( 2n - 4 \right) \times 90° \right\} = 3 \times \left( \frac{360° }{n} \times n \right)\]
\[ \Rightarrow \left( n - 2 \right) \times 180 = 3 \times 360\]
\[ \Rightarrow n - 2 = 6\]
\[ \therefore n = 8\]
APPEARS IN
संबंधित प्रश्न
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.
Complete of the following, so as to make a true statement:
A quadrilateral is convex if, for each side, the remaining ______ lie on the same side of the line containing the side.
The measure of angles of a hexagon are x°, (x − 5)°, (x − 5)°, (2x − 5)°, (2x − 5)°, (2x + 20)°. Find the value of x.
In a quadrilateral ABCD, AO and BO are bisectors of angle A and angle B respectively. Show that:
∠AOB = (∠C + ∠D)
In parallelogram ABCD, its diagonals intersect at point O. If OA = 6 cm and OB = 7.5 cm, find the length of AC and BD.

ABCDE is a pentagon in which AB is parallel to DC and ∠A : ∠E : ∠D = 1 : 2 : 3. Find angle A.
ΔPQR and ΔSQR are on the same base QR with P and S on opposite sides of line QR, such that area of ΔPQR is equal to the area of ΔSQR. Show that QR bisects PS.
What is the maximum number of obtuse angles that a quadrilateral can have?
Construct a quadrilateral NEWS in which NE = 7 cm, EW = 6 cm, ∠N = 60°, ∠E = 110° and ∠S = 85°.
An angle is said to be trisected, if it is divided into three equal parts. If in the following figure, ∠BAC = ∠CAD = ∠DAE, how many trisectors are there for ∠BAE?

