Advertisements
Advertisements
Question
One angle of a pentagon is 160° and the rest are all equal angles. Find the measure of the equal angles.
Solution
A pentagon has 5 sides
∴ Sum of interior angles
= (n - 2) x 180°
= (5 - 2) x 180°
= 3 x 180°
= 540°
One angle is given to be 160°
Ratio of the remaining four angles
= 1 : 1 : 1 : 1
∴ The interior angles are x°, x°, x° and x°
∴ 160° + x° + x° + x° + x° = 540°
⇒ 4x° = 540° - 160° = 380°
⇒ x° = 95°
∴ Each equal angle is 95°.
APPEARS IN
RELATED QUESTIONS
Given here are some figures:
 |
 |
 |
 |
 |
 |
 |
 |
Classify each of them on the basis of the following:
- Simple curve
- Simple closed curve
- Polygon
- Convex polygon
- Concave polygon
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:
The number of pairs of opposite angles of a quadrilateral is .......
Complete of the following, so as to make a true statement:
In a quadrilateral the point of intersection of the diagonals lies in .... of the quadrilateral.
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.
If the bisectors of two adjacent angles A and B of a quadrilateral ABCD intersect at a point O such that ∠C + ∠D = k ∠AOB, then find the value of k.
Which of the following quadrilateral is not a rhombus?
Two adjacent angles of a parallelogram are 70° and 110° respectively. Find the other two angles of it.
If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4, then ABCD is a ______.
If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S, then PQRS is a ______.
