Advertisements
Advertisements
प्रश्न
If two adjacent angles of a parallelogram are (5x – 5)° and (10x + 35)°, then the ratio of these angles is ______.
विकल्प
1 : 3
2 : 3
1 : 4
1 : 2
Advertisements
उत्तर
If two adjacent angles of a parallelogram are (5x – 5)° and (10x + 35)°, then the ratio of these angles is 1 : 3.
Explanation:
We know that, adjacent angles of a parallelogram are supplementary, i.e. their sum equals 180°.
∴ (5x – 5) + (10x + 35) = 180°
⇒ 15x + 30° = 180°
⇒ 15x = 150°
⇒ x = 10°
Thus, the angles are (5 × 10 – 5) and (10 × 10 + 35), i.e. 45° and 135°.
Hence, the required ratio is 45° : 135°, i.e. 1 : 3.
APPEARS IN
संबंधित प्रश्न
Consider the given parallelogram. Find the values of the unknowns x, y, z.
Can a quadrilateral ABCD be a parallelogram if ∠A = 70° and ∠C = 65°?
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.
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.
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.
The given figure shows parallelogram ABCD. Points M and N lie in diagonal BD such that DM = BN.
Prove that:
(i) ∆DMC = ∆BNA and so CM = AN
(ii) ∆AMD = ∆CNB and so AM CN
(iii) ANCM is a parallelogram.
Which of the following is a property of a parallelogram?
The adjacent sides of a parallelogram are 5 cm and 9 cm. Its perimeter is ______.
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
Find the values of x and y in the following parallelogram.
