Exterior Angle of a Triangle = Sum of Opposite Internal Angles

Q.

The measure of each exterior angle of a regular octagon is

1. ${90}^{\circ }$

2. ${180}^{\circ }$

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

4. ${60}^{\circ }$

Q.

In the given figure, If AB || CD, EF ⊥ CD and ∠GED = 126º, find ∠AGE, ∠GEF and ∠FGE.

Q.

In a regular polygon each interior angle is 120 degree grater than each exterior angle. Calculate the number of side of the polygon.

Q.

Calculate the number of sides of a regular polygon whose interior angle are each 156 degree

Q.

Find the measure of each exterior angle of an equilateral triangle.

Q.

In figure, $A,B,C$ and $D$ are four points on a circle. $AC$ and $BD$ intersect at a point $E$ such that $\angle BEC={130}^{\circ }$ and $\angle ECD={20}^{\circ }$. Find $\angle BAC$ (in degrees).

Q.

Find the value of x in the figure.

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

2. ${40}^{\circ }$

3. ${50}^{\circ }$

4. ${60}^{\circ }$

Q.

An exterior angle of triangle is ${80}^{\circ }$ and the interior opposite angles are in the ratio $1:3$. The measure of each interior opposite angle is

1. ${40}^{\circ },{120}^{\circ }$

2. ${20}^{\circ },{60}^{\circ }$

3. ${30}^{\circ },{60}^{\circ }$

4. ${30}^{\circ },{90}^{\circ }$

Q.

If the angles of a triangle are in the ratio 1 : 2 : 3, then the measure of the largest angle is ___.

1. 120°

2. 90°

3. 60°

4. 30°

Q.

In a triangle ABC, if AB = AC and AB is produced to D such that BD = BC, find $\angle ACD:\angle ADC.$

Q.

In the fig. below, if AB || CD, $\angle$APQ = 50${}^{\circ }$ and $\angle$PRD = 127${}^{\circ }$, find x and y.

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1. 50^o, 67^o

2. 50^o, 77^o

3. 77^o, 87^o

4. 77^o, 97^o

Q. In the given figure, $\angle$ACD is an exterior angle of $∆$ABC. $\angle$B = 40^°, $\angle$A = 70^°.

Find the measure of $\angle$ACD.

Q.

An exterior angle of a triangle is equal to ${100}^{\circ }$ and two interior opposite angles are equal. Each of these angles is equal to:

Q.

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the ____ interior opposite angles.

1. Three

2. One

3. Four

4. Two

Q.

In a triangle, an exterior angle at a vertex is ${95}^{\circ }$ and its one of the interior opposite angle is ${55}^{\circ }$ then the measure of the other interior angle is

1. ${40}^{\circ }$

2. ${9.0}^{\circ }$

3. ${55}^{\circ }$

4. ${85}^{\circ }$

Q.

An exterior angle of a triangle is ${110}^{\circ }$ and its two interior opposite angles are equal. Each of these equal angles is

$\left(a\right){70}^{\circ }$

$\left(b\right){55}^{\circ }$

$\left(c\right){35}^{\circ }$

$\left(d\right)27{\frac{1}{2}}^{\circ }$

Q.

In the figure, $AB$ divides $\angle DAC$ in the ratio $1:3$ and $AB=DB$. Determine the value of $x.$

Q.

State and prove the Angle Sum Property of a triangle .

Q.

Show that all the angles of an equilateral triangle are $60°$each.

Q.

An exterior angle of a triangle is 80^o and two interior opposite angles are equal. Measure of each of these angle is:

1. 100^o

2. 60^o

3. 40^o

4. 120^o

Q.

The exterior angles obtained on producing the base of a triangle both ways are ${104}^{\circ }$ and ${136}^{\circ }$ .Find all the angles of the triangle.

Q.

In triangle ABC if AD is bisector of angle A show that AB>BD and AC > DC

Q.

$Ina\Delta ABC,sideBCisproducedtoD.If\angle ABC={50}^{\circ }and\angle ACD={110}^{\circ }then\angle A=?\left(a\right){160}^{\circ }\left(b\right){60}^{\circ }\left(c\right){80}^{\circ }\left(d\right){30}^{\circ }$

Q.

In a $\Delta ABC,\angle A={50}^{\circ }$ and BC is produced to a point D. If the bisectors of $\angle ABC$ and $\angle ACD$ meet at E, then $\angle E$=

Q.

If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is:

1. ${180}^{\circ }$

2. ${270}^{\circ }$

3. ${360}^{\circ }$

4. ${90}^{\circ }$

Q.

In the figure, side BC of $\Delta ABC$ is peoduced to point D such that bisectors of $\angle ABC$ and $\angle ACD$ meet at a point E. If $\angle BAC={68}^{\circ }$, find $\angle BEC.$

Q.

$\text{In the given figure, side BC of}\Delta ABC\text{is produced to D.If}\angle ACD={128}^{\circ }and\angle ABC={43}^{\circ },find\angle BACand\angle ACB.$

Q.

An exterior angle of a triangle is ${108}^{\circ }$ and its its ineterior opposite angles are in are in the ratio 4 : 5 . The triangle are

Q.

Calculate the value of x in the given figure.

Q.

If the side BC of $\Delta ABC$ is produced on both sides, then write the difference between the sum of the exterior angles so formed and $\angle A.$