Exterior Angle Property

Q. Measures of angles of a triangle are x, 2x, 3x. What type of triangle is it?

Q.

Find the value of x in the given figure.

Q. One of the exterior angles of a triangle is ${80}^{\circ }$ and the interior opposite angles are in the ratio 3 : 5. Find the angles of the triangle.

Q. In the given figure MN and PQ are parallel, find $\text{X}+\text{Y}$.

1. 105

Q. In the given figure, if MN and PQ are parallel, find the value of $\text{X}+\text{Y}$ in degrees.

1. 105

Q.

The value of x in the given figure is ______.

1. 50^o
2. 80^o
3. 30^o
4. 40^o

Q. Which of the following statements are true$\left(T\right)$ and which are false$\left(F\right)$

$ix)$ An exterior angle of a triangle is less than either of its interior opposite angles.

Q.

An exterior angle of a triangle is 105^o and its two interior opposite angles are equal. Each of these equal interior angles is:

1. 52.5${}^{\circ }$

2. 37.5${}^{\circ }$

3. 72.5${}^{\circ }$

4. 75${}^{\circ }$

Q. In the given figure sides AB and AC of $\Delta$ABC are extended to points P and Q respectively. If $\angle PBC<\angle QCB$ then

1. AC > AB
2. AC < AB
3. AC = AB

Q.

In Fig. $\angle$E $>$$\angle$A and $\angle$C $>$$\angle$D. Prove that AD $>$EC. [2 MARKS]

Q. The angles of a pentagon in degrees are x, x + 20, x + 40, x + 60 and x + 80, then the smallest angle of the pentagon is

1. ${50}^o$
2. ${78}^o$
3. ${85}^o$
4. ${68}^o$

Q. In the given figure sides AB and AC of $\Delta$ABC are extended to points P and Q respectively. If $\angle PBC<\angle QCB$ then

1. AC > AB
2. AC < AB
3. AC = AB

Q.

In figure, $\angle ACD={120}^{\circ }$ and $\angle APB={100}^{\circ }$ ,
(i) find x and y.
(ii) If $\angle BAC=2.5y,$ find $\angle ABC$.

Q. $O$ is any point in the interior of $\Delta ABC.$ then
$AB+BC+CA<OA+OB+OC$ that is ?

1. True
2. False

Q. Sum of all interior and exterior angle of a triangle is equal to

Q. An exterior angle of a triangle is ${115}^{\circ }$ and one of the opposite angles is ${35}^{\circ }$. Find the other two angles.
(3 marks)

Q. In the given figure sides AB and AC of $\Delta$ABC are extended to points P and Q respectively. If $\angle PBC<\angle QCB$ then

1. AC > AB
2. AC < AB
3. AC = AB

Q.

In figure, $\angle ACD={120}^{\circ }$ and $\angle APB={100}^{\circ }$ ,
(i) find x and y.
(ii) If $\angle BAC=2.5y,$ find $\angle ABC$.

Q. An exterior angle of a triangle is 105 and its two interior opposite angles are equal. Each of these equal an gles is

Q. give reason
​
why the measure of single exterior angle is 360/n