Angle Sum Property of a Polygon

Q.

What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

Q. The angles of a quadrilateral are in the ratio 3:4:5:6. The largest angle of the quadrilateral is:​

1. 80°
2. 100°
3. 120°
4. 140°

Q. The sum of interior angles a convex polygon having 'n' sides is equal to .

1. n ×180°
2. (n-2) × 180°
3. (n-3) × 180°
4. (n-4) × 180°

Q.

In the given figure, x = ?

1. 25${}^{\circ }$

2. 35${}^{\circ }$

3. 45${}^{\circ }$

4. 55${}^{\circ }$

Q. Question 3
In the given figure, If $AB||CD,EF\perp CD$ and $\angle GED={126}^{\circ },$ find $\angle AGE,\angle GEFand\angle FGE.$

Q. The measure of the angles of a quadrilateral $ABCD$ are respectively in the ratio $1:2:3:4$. Then which of the following is true

1. $AC=BD$
2. $AD\parallel BC$
3. $AB\parallel DC$
4. $noneofthese$

Q. Question 6
Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Q. M is the midpoint of side PQ of a parallelogram PQRS. A line through Q parallel to MS meets SR at N and PS produced at L. Prove that QL = 2QN.

Q. Question 1
The angle of quadrilateral are in the ratio 3 : 5 : 9 :13. Find the all the angles of the quadrilateral.

Q. $\Delta$BUG is an isosceles triangle with BU = GU. Find all the angles.

1. ${50}^{\circ }$, ${50}^{\circ }$, ${80}^{\circ }$
2. ${45}^{\circ }$, ${45}^{\circ }$, ${90}^{\circ }$
3. ${42}^{\circ }$, ${42}^{\circ }$, ${96}^{\circ }$
4. ${60}^{\circ }$, ${30}^{\circ }$, ${90}^{\circ }$

Q. The measure of each exterior angle of a regular polygon of 15 sides is:

1. 24 degrees
2. 156 degrees
3. 360 degrees
4. 280 degrees

Q. Which of the following pair of angles are alternate exterior angles in the given figure?

1. ∠PXA and ∠QYD
2. ∠YXB and ∠XYC
3. ∠QYD and ∠QXA
4. ∠YXB and ∠PXA

Q. The angles of a quadrilateral are in the ratio 3:4:5:6. Find the angles of the quadrilateral.

Q.

1. AB = 8.5cm = Dc, BC = 8.5cm = DA

2. AB = 9.5cm = DC, BC = 5.5 cm = DA

3. AB = BC = DC = DA = 9.5cm

4. AB = 6.7 cm = BC, DC = DA = 5.7cm

Q. In the figure, ABCP is a parallelogram and P is the midpoint of CD. Which of the following is correct?​

1. $OA=\frac{1}{2}CD$
2. $AP=\frac{1}{2}BC$
3. $OB=\frac{1}{2}BD$
4. $PD=AP$

Q. Find the value of PQ if PM:MQ = 2:3.

1. 5 cm
2. 8 cm
3. 16 cm
4. 20 cm

Q. In the figure, ABCP is a parallelogram and P is the midpoint of CD. Which of the following is correct?​

Q. If in a kite ABCD, AB = 3 cm and BC = 5 cm, then find the value of AD + CD.

1. 3 cm
2. 5 cm
3. 8 cm
4. 10 cm

Q. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Q. If the angles of a quadrilateral are in the ratio 3:4:5:6, then find the angles of the quadrilateral.

1. ${60}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$, ${120}^{\circ }$
2. ${120}^{\circ }$, ${100}^{\circ }$, ${80}^{\circ }$, ${60}^{\circ }$
3. ${120}^{\circ }$, ${60}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$
4. ${80}^{\circ }$, ${100}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$

Q. The measures of five angles of a hexagon are equal and the sixth measure ${100}^0$. Then the measure of each of the five angle is

1. ${130}^0$
2. ${120}^0$
3. ${124}^0$
4. ${128}^0$

Q. Two angles are complementary. If the larger angle is twice the measure of a smaller angle, then smaller is _____

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${15}^{\circ }$

Q. In the figure, if $\angle A+\angle B+\angle C+\angle D+\angle E+\angle F=k\times$ right angle, then $k$ is :

1. $2$
2. $3$
3. $4$
4. $5$

Q. A quadrilateral has there acute angles, what will be the type of the fourth angle?

1. Acute
2. Obtuse
3. Right
4. None

Q. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see the given figure). Show that the line segments AF and EC trisect the diagonal BD.

Q. The angles of a quadrilateral are $x^{\circ },(x-10{)}^{\circ },(x+30{)}^{\circ }$ and $(2x{)}^{\circ }$. Find the value of the greatest angle. (2 marks)

Q. An angle is ${34}^o$ less than its supplement. The measure of the angle is

1. ${148}^o$
2. None of these
3. ${37}^o$
4. ${74}^o$

Q.

The complementary angle of an angle is greater than twice of it by 21°. Find the measure of the angle.

1. 27°
2. 29°
3. 21°
4. 23°

Q.

The angles of a quadrilateral are in the ratio 1:2:3:4. Find all the angles of the quadrilateral. [3 MARKS]

Q. Which of the following pair of angles are alternate exterior angles in the given figure?

1. ∠PXA and ∠QYD
2. ∠QYD and ∠QXA
3. ∠YXB and ∠XYC
4. ∠YXB and ∠PXA