Advertisements
Advertisements
Question
If the ratio of measures of two adjacent angles of a parallelogram is 1 : 2, find the measures of all angles of the parallelogram.
Advertisements
Solution
Let `square`ABCD be the parallelogram.
The ratio of measures of two adjacent angles of a parallelogram is 1 : 2.
Let the common multiple be x.
∴ ∠A = x° and ∠B = 2x°
∠A + ∠B = 180° ...[Adjacent angles of a parallelogram are supplementary]
∴ x + 2x = 180
∴ 3x = 180
∴ x = `180/3`
∴ x = 60
∠A = x° = 60°
∠B = 2x°
= 2 × 60° = 120°
∠A = ∠C = 60°
∠B = ∠D= 120° ...[Opposite angles of a parallelogram]
APPEARS IN
RELATED QUESTIONS
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.
Consider the given parallelograms. Find the values of the unknowns x, y, z.
Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
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 adjacent figure, if seg AB || seg PQ, seg AB ≅ seg PQ, seg AC || seg PR, seg AC ≅ seg PR then prove that, seg BC || seg QR and seg BC ≅ seg QR.
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.
ABCD is a parallelogram. What kind of quadrilateral is it if : AC = BD and AC is perpendicular to BD?
In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.
Use the information given in the alongside diagram to find the value of x, y, and z.
The adjacent sides of a parallelogram are 5 cm and 9 cm. Its perimeter is ______.
ABCD is a parallelogram. Find the value of x, y and z.
Construct a parallelogram ABCD in which AB = 4 cm, BC = 5 cm and ∠B = 60°.
Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.
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.
