Advertisements
Advertisements
प्रश्न
The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.
Advertisements
उत्तर
Let the measures of two adjacent angles, ∠A and ∠B, of parallelogram ABCD are in the ratio of 3 : 2. Let ∠A = 3x and ∠B = 2x
We know that the sum of the measures of adjacent angles is 180º for a parallelogram.
∠A + ∠B = 180º
3x + 2x = 180º
5x = 180º
`x = 180^circ/5 = 36`
∠A = ∠C = 3x = 108º (Opposite angles)
∠B = ∠D = 2x = 72º (Opposite angles)
Thus, the measures of the angles of the parallelogram are 108º, 72º, 108º, and 72º
APPEARS IN
संबंधित प्रश्न
Can a quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180°?
Can a quadrilateral ABCD be a parallelogram if AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?
The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
In the given figure, if points P, Q, R, S are on the sides of parallelogram such that AP = BQ = CR = DS then prove that `square`PQRS is a parallelogram.
ABCD is a parallelogram. What kind of quadrilateral is it if : AC = BD and AC is perpendicular to BD?
Prove that the diagonals of a parallelogram bisect each other.
In the given figure, AB || EC, AB = AC and AE bisects ∠DAC. Prove that:
- ∠EAC = ∠ACB
- ABCE is a parallelogram.
The adjacent sides of a parallelogram are 5 cm and 9 cm. Its perimeter is ______.
ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is AXCY a parallelogram? Give reason.
A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.
