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
Can a quadrilateral ABCD be a parallelogram if ∠A = 70° and ∠C = 65°?
In the above figure both RISK and CLUE are parallelograms. Find the value of x.
Find the measure of ∠P and ∠S, if `bar(SP) || bar(RQ)` in the following figure. (If you find m∠R, is there more than one method to find m∠P?).
Name the quadrilaterals whose diagonals bisect each other
If the ratio of measures of two adjacent angles of a parallelogram is 1 : 2, find the measures of all angles of the parallelogram.
In the given figure, `square`ABCD is a parallelogram. Point E is on the ray AB such that BE = AB then prove that line ED bisects seg BC at point F.
Ratio of two adjacent sides of a parallelogram is 3 : 4, and its perimeter is 112 cm. Find the length of its each side.
Referring the adjacent figure of a parallelogram, write the answer of questions given below.
(1) If l(WZ) = 4.5 cm then l(XY) = ?
(2) If l(YZ) = 8.2 cm then l(XW) = ?
(3) If l(OX) = 2.5 cm then l(OZ) = ?
(4) If l(WO) = 3.3 cm then l(WY) = ?
(5) If m∠WZY = 120° then m∠WXY = ? and m∠XWZ = ?
In parallelogram PQRS, ∠Q = (4x – 5)° and ∠S = (3x + 10)°. Calculate: ∠Q and ∠R.
PQRS is a parallelogram whose diagonals intersect at M.
If ∠PMS = 54°, ∠QSR = 25° and ∠SQR = 30° ; find :
(i) ∠RPS
(ii) ∠PRS
(iii) ∠PSR.
Prove that the diagonals of a parallelogram bisect each other.
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 e
If two adjacent angles of a parallelogram are (5x – 5)° and (10x + 35)°, then the ratio of these angles is ______.
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
In parallelogram LOST, SN ⊥ OL and SM ⊥ LT. Find ∠STM, ∠SON and ∠NSM.
Find the values of x and y in the following parallelogram.
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.
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.
In the following figure, FD || BC || AE and AC || ED. Find the value of x.
Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.
