Exterior and Interior Points to an Angle

Q.

If the exterior angle of a regular polygon is one-fifth of the interior angle then find the value of the exterior angle.

1. 30${}^{\circ }$

2. 90${}^{\circ }$

3. 60${}^{\circ }$

4. 45${}^{\circ }$

Q. Which point is interior to $\angle$$ABC$?

1. P
2. Q
3. R
4. None of these

Q. Is it possible to have a regular polygon whose each interior angle is :
${170}^o$

Q. If the difference between an exterior angle of an (n - 1) sided regular polygon and an (n + 1) sided regular polygon is $9^{\circ }$, the find the value of ‘n’.

Q. i) one common point
ii) two common points
iii) three common points
iv) four commmon points.

Q.

In the figure, ABCD is a quadrilateral in which \(\angle ADC=105^\circ ~and~ \angle ADC=~\angle ABC. Find \angle CBE\).

Q. If one of the interior angles of a regular polygon is found to be equal to $\frac{9}{8}$ times of one of the interior angles of a regular hexagon, then the number of sides of the polygon is

Q. Let $S$ be the sum of the interior angles of a polygon $P$ for which each interior angle is $7\frac{1}{2}$ times the exterior angle at the same vertex. Then

1. $S={2660}^{\circ }$ and $P$ may be regular
2. $S={2660}^{\circ }$ and $P$ is not regular
3. $S={2700}^{\circ }$ and $P$ is regular
4. $S={2700}^{\circ }$ and $P$ is not regular
5. $S={2700}^{\circ }$ and $P$ may or may not be regular

Q. If any interior angle of a regular polygon exceeds the exterior angle by 100, then the number of sides of the polygon is

1. 7
2. 8
3. 9
4. 6

Q. At least one of the internal angles of a concave polygon is greater than 180${}^{\circ }$.

1. True

2. False

Q. The sum of the outer angles of polygon is twice the sum of the inner angles.

1. (i) $3$ (ii) $4$ (iii) $6$
2. (i) $4$ (ii) $3$ (iii) $6$
3. (i) $3$ (ii) $6$ (iii) $4$
4. (i) $6$ (ii) $4$ (iii) $3$

Q. Sum of interior angle of a regular polygon is equal to six times the sum of exterior angle. Find the no. of sides.

Q. In $\Delta PQR,\angle Q={72}^o$ and $\angle P={45}^o$. Then find exterior angle $\angle x$.

1. ${127}^o$
2. ${63}^o$
3. ${117}^o$
4. ${53}^o$

Q. If x = 20 and y = 30 in the figure above, what is the value of z ?

1. 60
2. 70
3. 80
4. 90
5. 100

Q. The sum of all the angles of a pentagon are

1. ${360}^o$
2. ${540}^o$
3. ${720}^o$
4. none of these