Advertisements
Advertisements
Question
In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.
Advertisements
Solution
We have, two parallelograms ABDH and CEFG.
Now, In ABDH,
∴ ∠ABD = ∠AHD = 130° ...[∵ Opposite angles of a parallelogram are equal]
And ∠GHD = 180° – ∠AHD
= 180° – 130° ...[Linear pair]
⇒ ∠GHO = 50°
Also, ∠EFG + ∠FGC = 180° ...[∵ Adjacent angles of a parallelogram are supplementary]
⇒ 30° + ∠FGC = 180°
⇒ ∠FGC = 180° – 30° = 150°
And ∠HGC + ∠FGC = 180° ...[Linear pair]
∠HGC = 180° – ∠FGC
= 180° – 150°
∴ ∠HGO = 30°
In ΔHGO, by using angle sum property,
∠OHG + ∠HGO + ∠HOG = 180°
⇒ 50° + 30° + x = 180°
⇒ x = 180° – 80°
= 100°
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 = ______
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.
If the ratio of measures of two adjacent angles of a parallelogram is 1 : 2, find the measures of all angles of the parallelogram.
Given: Parallelogram ABCD in which diagonals AC and BD intersect at M.
Prove: M is the mid-point of LN.
ABCD is a parallelogram. What kind of quadrilateral is it if: AC is perpendicular to BD but is not equal to it?
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
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. Points P and Q are taken on the sides AB and AD respectively and the parallelogram PRQA is formed. If ∠C = 45°, find ∠R.
In parallelogram ABCD, the angle bisector of ∠A bisects BC. Will angle bisector of B also bisect AD? Give reason.
