# The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is $60^o$, find the other angles.

Given:

The opposite sides of a quadrilateral are parallel and one angle of the quadrilateral is $60^o$.

To do:

We have to find the other angles.

Solution:

Let $AB \parallel DC$ and $AD \parallel BC$ and $\angle A = 60^o$ in quadrilateral $ABCD$.

$AB \parallel DC$ and $AD \parallel BC$

This implies,

$ABCD$ is a parallelogram.

Therefore,

$\angle A + \angle B = 180^o$ (Co-interior angles are supplementary)

$60^o + \angle B = 180^o$

$\angle B = 180^o-60^o= 120^o$

Opposite angles of a parallelogram are equal.

Therefore,

$\angle C = \angle A = 60^o$

$\angle D = \angle B = 120^o$

**Hence, the other angles are $120^o, 60^o$ and $120^o$.**

- Related Articles
- In a cyclic quadrilateral $ABCD$, if $\angle A - \angle C = 60^o$, prove that the smaller of two is $60^o$.
- Find the measure of each of the angles of the quadrilateral whose each pair of adjacent sides are equal and when angle is $90^{o}$.
- The angles of a quadrilateral are in A.P. whose common difference is $10^o$. Find the angles.
- If the angles of a quadrilateral are $4x, 3x+10^o, 2x+10^o$ and $4x+15^o$, then find the angles.
- If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that is diagonals are equal.
- ABCD is a cyclic quadrilateral (see figure). Find the angles of the cyclic quadrilateral."
- If the sides of a quadrilateral touch a circle, prove that the sum of a pair of opposite sides is equal to the sum of the other pair.
- The angles of quadrilateral are in the ratio $3: 5: 9: 13 $ Find all the angles of the quadrilateral.
- In a quadrilateral angles are in the ratio 2:3:4:7 . Find all the angles of the quadrilateral. Is it a convex or a concave quadrilateral
- If one of the complementary angles is twice the other, the two angles areĀ a) $60^o, 30^o$b) $20^o, 60^o$c) $40^o, 40^o$d) $10^o, 70^o$
- In a cyclic quadrilateral $ABCD$, if $AB \| CD$ and $\angle B = 70^o$, find the remaining angles.
- Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
- Show that the line segments joining the mid points of the opposite sides of a quadrilateral bisect each other.
- Three angles of a quadrilateral are respectively equal to $110^o, 50^o$ and $40^o$. Find its fourth angle.
- Two angles of a quadrilateral are $3x\ -\ 4$ each and two are $3x\ +\ 10$ each. Find all four angles of the quadrilateral.

##### Kickstart Your Career

Get certified by completing the course

Get Started