Exercise 12
Question 1
1. The three angles of a quadrilateral are $65^{\circ}, 55^{\circ}$ and $130^{\circ}$. Find its fourth angle.
2. The two adjacent angles of a quadrilateral are $75^{\circ}$ and $125^{\circ}$. The other two angles are equal. Find the measure of each of these equal angles.
3. In a quadrilateral $A B C D, \angle A=150^{\circ}$ and $\angle B=\angle C=\angle D$, find $\angle B, \angle C$ and $\angle D$.
4. In the adjoining figure, $P$ is a point in the interior of $\angle A O B$ and $\angle A O B=40^{\circ}$. If $P M \perp O A$ and $P N \perp O B$, find the measure of $\angle M P N$.
5. A quadrilateral has all four angles of the same measure, what is the measure of each angle ?
6. Two angles of a quadrilateral measure $55^{\circ}$ each. The third angle is $140^{\circ}$. What is the measure of the fourth angle ?
7. Find the measures of the four angles of a quadrilateral if they are in the ratio $3: 5: 7: 9$.
8. $A B C D$ is a quadrilateral. $A O$ and $B O$ are the angle bisectors of angle $A$ and $B$ which meet at $O$. If $\angle C=70^{\circ}, \angle D=50^{\circ}$, find $\angle A O B$.
Multiple Choice Questions (MCQs)
9. The fourth angle of the quadrilateral that has three acute angles is
(a) acute
(b) right
(c) obtuse
(d) straight
10. The value of y in the given figure is :
(a) 89°
(b) 91°
(c) 101°
(d) 79°
11.What is the value of a ?
(a) 90°
(b) 10°
(c) 180°
(d) 2°
High Order Thinking Skills (HOTS)
12.Find the values of x, y and z in the diagram. Give reasons wherever necessary.
<figure to be added>
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