Advertisements
Advertisements
प्रश्न
In parallelogram MODE, the bisector of ∠M and ∠O meet at Q, find the measure of ∠MQO.
उत्तर
Let MODE be a parallelogram and Q be the point of intersection of the bisector of ∠M and ∠O.
Since, MODE is a parallelogram
∴ ∠EMO + ∠DOM = 180° ...[∵ Adjacent angles are supplementary]
⇒ `1/2` ∠EMO + `1/2` ∠DOM = 90° ...[Dividing both sides by 2]
⇒ ∠QMO + ∠QOM = 90° ...(i)
Now, In ΔMOQ,
∠QOM + ∠QMO + ∠MQO = 180° ...[Angle sum property of triangle]
⇒ 90° + ∠MQO = 180° ...[From equation (i)]
∴ ∠MQO = 180° – 90° = 90°
APPEARS IN
संबंधित प्रश्न
Given a parallelogram ABCD. Complete each statement along with the definition or property used.
- AD = ______
- ∠DCB = ______
- OC = ______
- m∠DAB + m∠CDA = ______
Perimeter of a parallelogram is 150 cm. One of its sides is greater than the other side by 25 cm. Find the lengths of all sides.
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.
Ratio of two adjacent sides of a parallelogram is 3 : 4, and its perimeter is 112 cm. Find the length of its each side.
Construct a parallelogram ABCD such that l(BC) = 7 cm, m∠ABC = 40° , l(AB) = 3 cm.
In parallelogram ABCD, X and Y are midpoints of opposite sides AB and DC respectively. Prove that:
(i) AX = YC
(ii) AX is parallel to YC
(iii) AXCY is a parallelogram.
In the given figure, AB || EC, AB = AC and AE bisects ∠DAC. Prove that:
- ∠EAC = ∠ACB
- ABCE is a parallelogram.
Which of the following figures satisfy the following properties?
- All sides are congruent.
- All angles are right angles.
- Opposite sides are parallel.
ABCD is a parallelogram. Find the value of x, y and z.
The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 45°. Find the angles of the parallelogram.
