Angles of a Parallelogram

Q.

The adjacent angles of a parallelogram are___.

Q. If ABCD is a parallelogram, then the angle bisectors of $\angle A$ and $\angle D$ meet at ‘O’. The measure of $\angle AOD$ is ${45}^{\circ }$​.

1. 
2. 

Q. The diagnols of a parallelogram $PQRS$ are along the line $x+3y=4$ and $6x-2y=7$ then $PQRS$ must be a

1. reactangle
2. square
3. cyclic quadriletral
4. rhombus

Q. In the adjoining figure, name the following pairs of angles.
Adjacent complementary angles.

Q. The length of longer diagonal of the parallelogram on $5\overline{a}+2\overline{b}$ and $\overline{a}-3\overline{b}$. if it is given $\left|\overline{a}\right|=2\sqrt{2}:\left|\overline{b}\right|=3$ and $\left(\overline{a},\overline{b}\right)=\pi /4$ is

1. $15$
2. $\sqrt{113}$
3. $\sqrt{593}$
4. $\sqrt{395}$

Q. In the given figure, $E$ is mid-point of $AB$ and $DE$ meets diagonal $AC$ at point $F$.
If $ABCD$ is a parallelogram and area of $△ADF$ is $60c{m}^2$, then area of $△ADB$ is?