Advertisements
Advertisements
प्रश्न
In the given figure, `square`PQRS and `square`ABCR are two parallelograms. If ∠P = 110° then find the measures of all angles of `square`ABCR.
Advertisements
उत्तर
`square`PQRS is a parallelogram. ...[Given]
∴ ∠R = ∠P ...[Opposite angles of a parallelogram]
∴ ∠R = 110° ...(i)
`square`ABCR is a parallelogram. ...[Given]
∴ ∠A + ∠R = 180° ...[Adjacent angles of a parallelogram are supplementary]
∴ ∠A + 110° = 180° ...[From (i)]
∴ ∠A = 180° - 110°
∴ ∠A = 70°
∴ ∠C = ∠A = 70°
∴ ∠B = ∠R = 110° ...[Opposite angles of a parallelogram]
∴ ∠A = 70°, ∠B = 110°,
∴ ∠C = 70°, ∠R = 110°
APPEARS IN
संबंधित प्रश्न
Consider the given parallelogram. Find the values of the unknowns x, y, z.
Consider the given parallelograms. Find the values of the unknowns x, y, z.
Can a quadrilateral ABCD be a parallelogram if AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?
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.
In the above figure both RISK and CLUE are parallelograms. Find the value of x.
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.
ABCD is a parallelogram. What kind of quadrilateral is it if : AC = BD and AC is perpendicular to BD?
ABCD is a parallelogram. What kind of quadrilateral is it if: AC = BD but AC is not perpendicular to BD?
In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD. Prove that:
- AE = AD,
- DE bisects and ∠ADC and
- Angle DEC is a right angle.
The given figure shows parallelogram ABCD. Points M and N lie in diagonal BD such that DM = BN.
Prove that:
(i) ∆DMC = ∆BNA and so CM = AN
(ii) ∆AMD = ∆CNB and so AM CN
(iii) ANCM is a parallelogram.
Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between d and f
Which of the following figures satisfy the following properties?
- All sides are congruent.
- All angles are right angles.
- Opposite sides are parallel.
In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then ∠BEC = ______.
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
Find the values of x and y in the following parallelogram.
Two angles of a quadrilateral are each of measure 75° and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.
A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.
Construct a parallelogram when one of its side is 4 cm and its two diagonals are 5.6 cm and 7 cm. Measure the other side.
