Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let ABCD be a quadrilateral,
Where ∠A = ∠C = 75° and ∠B = ∠D = x ...[say]
Then, by the angle sum property of a quadrilateral, we have
∠A + ∠B + ∠C + ∠D = 360°
⇒ 75° + x + 75° + x = 360°
⇒ 2x = 360° – 150°
⇒ 2x = 210°
⇒ x = 105°
Thus, other two angles are 105° each.
Since, opposite angles are equal, therefore the quadrilateral is a parallelogram.
APPEARS IN
RELATED QUESTIONS
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.
PQRS is a parallelogram whose diagonals intersect at M.
If ∠PMS = 54°, ∠QSR = 25° and ∠SQR = 30° ; find :
(i) ∠RPS
(ii) ∠PRS
(iii) ∠PSR.
Given: Parallelogram ABCD in which diagonals AC and BD intersect at M.
Prove: M is the mid-point of LN.
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 b and c
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 c and f
The adjacent sides of a parallelogram are 5 cm and 9 cm. Its perimeter is ______.
All rectangles are parallelograms.
Find the values of x and y in the following parallelogram.
In parallelogram ABCD, the angle bisector of ∠A bisects BC. Will angle bisector of B also bisect AD? Give reason.
Construct a parallelogram ABCD in which AB = 4 cm, BC = 5 cm and ∠B = 60°.
