Angle Sum Property of a Polygon

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.

1. None of the above
2. ${136}^{\circ }$
3. ${180}^{\circ }$
4. ${68}^{\circ }$

Q.

The three angles of a quadrilateral are ${75}^{\circ }$, ${90}^{\circ }$ and ${75}^{\circ }$. The fourth angle is:

1. 120°

2. 90°

3. 95°

4. 105°

Q.

During the construction of a quadrilateral for which 2 sides and 3 angles are known, how can the fourth point be located?

1. Using the angle and the length

2. Using only the length

3. Using the arcs

4. Using 2 angles

Q. Find the angle measure x in each of the following figures.

Q. The angles of a quadrilateral are in A.P whose common difference is ${10}^{\circ }$. Find the angles.

1. ${70}^{\circ },{80}^{\circ },{90}^{\circ },{100}^{\circ }$
2. ${60}^{\circ },{80}^{\circ },{100}^{\circ },{120}^{\circ }$
3. ${75}^{\circ },{85}^{\circ },{95}^{\circ },{105}^{\circ }$
4. ${72}^{\circ },{85}^{\circ },{98}^{\circ },{111}^{\circ }$

Q. The supplement of five-sixth of a right angle is:

1. $5^{\circ }$
2. ${95}^{\circ }$
3. ${126}^{\circ }$
4. ${105}^{\circ }$

Q. In a quadrilateral $ABCD$, $\angle D={90}^o$ & $\angle A=\angle B=\angle C$, find $\angle A$.

1. $100$
2. $110$
3. $90$
4. $80$

Q. ABCD is a parallelogram in which $\angle DAO={40}^{\circ }$, $\angle BAO={35}^{\circ }and\angle COD={65}^{\circ }$ . Find $\angle ODC$.

Q.

The sum of interior angles of a quadrilateral is ___ degrees.

Q. If the sum of three equal angles is 180° , then each angle will be _____.

1. 60°
2. 120°
3. 90°
4. 30°

Q. Find the complementary angle pair among the following

1. ${65}^o$
2. ${25}^o$
3. ${89}^o$
4. ${40}^o$

Q.

The three angles of the quadrilateral are 55°, 65°, and 105°. What is the fourth angle ?

1. 125°
2. 105°
3. 135°
4. 115°