Advertisements
Advertisements
Question
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.
Solution
`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
RELATED QUESTIONS
Given a parallelogram ABCD. Complete each statement along with the definition or property used.
- AD = ______
- ∠DCB = ______
- OC = ______
- m∠DAB + m∠CDA = ______
Can a quadrilateral ABCD be a parallelogram if ∠A = 70° and ∠C = 65°?
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?).
Construct ☐ PQRS, such that l(PQ) = 3.5 cm, l(QR) = 5.6 cm, l(RS) = 3.5 cm, m∠Q = 110°, m∠R = 70°. If it is given that ☐ PQRS is a parallelogram, which of the given information is unnecessary?
Construct ☐ BARC such that l(BA) = l(BC) = 4.2 cm, l(AC) = 6.0 cm, l(AR) = l(CR) = 5.6 cm
Ratio of consecutive angles of a quadrilateral is 1 : 2 : 3 : 4. Find the measure of its each angle. Write, with reason, what type of a quadrilateral it is.
ABCD is a parallelogram. What kind of quadrilateral is it if: AC is perpendicular to BD but is not equal to it?
If a triangle and a parallelogram lie on the same base and between the same parallels, then prove that the area of the triangle is equal to half of the area of parallelogram
The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is ______.
ABCD is a parallelogram. Find the value of x, y and z.
