Exterior Angle of a Triangle and Its Property

Q. The line joining the centre of a circle to the mid-point of a chord is always perpendicular to the chord. True or False?

1. True
2. False

Q.

In the given figure, POQ is a line, then the value of 'x' is

1. 
2. 
3. 
4. 

Q.

Question 126

Find the value of x in the given figure.

Q.

In the above figure, ABCD is a square and BCE is an equilateral triangle, what is the measure of angle DEC?

1. ${15}^{\circ }$
2. ${30}^{\circ }$
3. ${20}^{\circ }$
4. ${45}^{\circ }$

Q.

If $(a+3b)(3a+b)=4h^2$then the angle between the lines represented by $a{x}^2+2hxy+b{y}^2=0$ is

1. ${30}^0$

2. ${45}^0$

3. ${60}^0$

4. ${\tan }^{-1}(½)$

Q.

Question 119

Find the measure of $\angle A$ in the given figure.

Q.

Question 1 (i)
Find the value of the unknown exterior angle x in the following diagrams:

Q.

ABC is a triangle in which AB = AC. The base BC is produced to D and $\angle ACD={130}^{\circ }$. Then $\angle A$ equals

1. ${80}^{\circ }$
2. ${60}^{\circ }$
3. ${50}^{\circ }$
4. ${40}^{\circ }$

Q.

Question 19

In the given figure, BC = CA and $\angle A={40}^{\circ }$. Then, $\angle ACD$ is equal to

a) ${40}^{\circ }$
b) ${80}^{\circ }$
c) ${120}^{\circ }$
d) ${60}^{\circ }$

Q.

Question 41

In $\Delta ABC$, $\angle A={50}^{\circ },\angle B={70}^{\circ }$ and bisector of $\angle C$ meets AB at D as shown in the given figure. Measure of $\angle ADC$ is

a) ${50}^{\circ }$
b) ${100}^{\circ }$
c) ${30}^{\circ }$
d) ${70}^{\circ }$

Q.

Exterior angle and its adjacent interior angle form a ____________.

Q.

Question 124

In $\Delta ABC$, if $\angle A=\angle C$ and exterior $\angle ABX={140}^{\circ }$, then find the angles of the triangle.

Q.

Question 34

The measures of $\angle x$ and $\angle y$ in the given figure are respectively.

a) ${30}^{\circ },{60}^{\circ }$
b) ${40}^{\circ },{40}^{\circ }$
c) ${70}^{\circ },{70}^{\circ }$
d) ${70}^{\circ },{60}^{\circ }$

Q.

Consider the figure:

If BC = AC and angle ACB = 60^o, then find the value of $\angle$A + $\angle$B + $\angle$x + $\angle$y .

___

Q.

Consider the figure:

If $\angle$B = ${50}^{\circ }$, $\angle$ACD = ${120}^{\circ }$, then the value of $\angle$A (in degrees) is .

Q.

Question 145 (i)

In the given figure, it is given that LM = ON and NL = MO

State the three pairs of equal parts in the $\Delta NOM$ and $\Delta MLN$

Q.

In the figure, the bisector of B and C meet at O. Then ∠BOC is

1. 

2. 

3. 

4. 

Q.

Question 2 (iii)
Find the value of the unknown interior angle x in the following figures.

Q.

Question 144 (ii)

ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (see the figure)

Is $\Delta ABD\cong \Delta ACD$? If so why?

Q.

Question 1 (iv)
Find the value of the unknown exterior angle x in the following diagrams:

Q.

Question 1 (v)
Find the value of the unknown exterior angle x in the following diagrams:

Q.

Question 2 (vi)
Find the value of the unknown interior angle x in the following figures.

Q.

Question 33

In the given figure, $a={40}^{\circ }$. The value of b is

(a) ${20}^{\circ }$
(b) ${24}^{\circ }$
(c) ${36}^{\circ }$
(d) ${120}^{\circ }$

Q. Prove that sum of all interior angles in the shown triangle is equal to ${180}^{\circ }$

Q.

Consider the figure:

If $\angle$B = ${50}^{\circ }$, $\angle$ACD = ${120}^{\circ }$, and x = 2y, then find the value of $\angle$A (in degrees).

___

Q.

In the figure given here, lines $l,m$ and $n$ are parallel to each other and $p$ is transversal. Find $x$ and $y$.

Q. In ABC, If BC=AB and $\angle B={80}^{\circ }$, then $\angle A$ is equal to:

1. ${80}^{\circ }$
2. ${40}^{\circ }$
3. ${50}^{\circ }$
4. ${100}^{\circ }$

Q.

In the above figure, $\angle BOC$ = x + y. Say True or False

1. False

2. True

Q.

If a side of a triangle is produced, the angle so formed is equal to the sum of the two_______________.

Q. An isosceles right angled triangle has area $8c{m}^2$. Find the length of its hypotenuse.