Calculating Angles

Q. In an isosceles triangle ABC, AB = AC and BA is produced to D, such that AB = AD. What is the value of $\angle BCD$?

1. ${70}^{\circ }$
2. ${90}^{\circ }$
3. ${60}^{\circ }$
4. ${45}^{\circ }$

Q. Question 1
In figure, if $\angle BAC={90}^{\circ }andAD\perp BC$. Then,


(A) $BD.CD=B{C}^2$
(B) $AB.AC=B{C}^2$
(C) $BD.CD=A{D}^2$
(D) $AB.AC=A{D}^2$

Q.

Question 123

If the sides of a triangle are produced in an order, show that the sum of the exterior angles so formed is ${360}^{\circ }$

Q. In the given figure, the value of 'x' and 'y' is:

1. $x={45}^{\circ },y={65}^{\circ }$
2. $x={125}^{\circ },y={65}^{\circ }$
3. $x={75}^{\circ },y={45}^{\circ }$
4. $x={125}^{\circ },y={35}^{\circ }$

Q. Find angles x and y, as show in the figure.

Q. In the given figure, find the value of $x$ (in degrees).

1. 71
2. 61
3. 63
4. 73

Q.

In the given figure, T is a point on side QR of $\Delta PQR$ and S is a point such that RT = ST.
Which of the following is true?

1. PQ + PR > QS
2. PQ + TR > QS
3. PQ + TR < QS
4. PQ + PR < QS

Q.

Find angles x and y.

1. $x={47}^{\circ },y={25}^{\circ }$

2. $x={27}^{\circ },y={45}^{\circ }$

3. $x={45}^{\circ },y={27}^{\circ }$

4. $x={25}^{\circ },y={47}^{\circ }$

Q.

If the side of a triangle are produced as shown in the figure, then x + y + z = ____.

1. 180°

2. 360°

3. 90°

4. 270°

Q.

If 'a' and 'b' are two angles of a triangle, then the third angle will be 180 - (a+b) degrees.

1. 180

2. 90

Q. Find the $\angle ACB$, as shown in the figure.

Q.

In the figure, sides $QP$ and $RQ$ of $△PQR$ are produced to points S and T, respectively. If $\angle SPR={135}^{\circ }$ and $\angle PQT={110}^{\circ }$, find $2\angle PRQ.$

1. ${150}^{\circ }$
2. ${110}^{\circ }$
3. ${90}^{\circ }$
4. ${130}^{\circ }$

Q.

In $△ABC$, if $BC=AB$ and $\angle B=80°$, then $\angle A$ is equal to :

Q.

If the angles of a triangle are $x^{\circ }$, $2x^{\circ }$​ and $3x^{\circ }$, then the value of x is __ (in degrees).

Q.

Angle ADC measures ___.

1. 120°

2. 90°

3. 60°

4. 30°

Q. Find angles x and y, as show in the figure.

Q.

In the figure given, if AB || CD, Find the values of 'p' and 'q'.

1. ${75}^{\circ }$ and ${20}^{\circ }$

2. ${20}^{\circ }$ and ${75}^{\circ }$

3. ${25}^{\circ }$ and ${70}^{\circ }$

4. ${70}^{\circ }$ and ${25}^{\circ }$

Q.

Two triangles are of the same shape. The sum of both their internal angles is ___ degrees.

1. ${180}^{\circ }$
2. ${270}^{\circ }$
3. ${360}^{\circ }$
4. ${450}^{\circ }$

Q. Each angle in an equilateral triangle is .

1. 45${}^{\circ }$
2. 60${}^{\circ }$
3. 75${}^{\circ }$

Q.

In an isosceles $\Delta ABC$, $\angle A$ is ${30}^{\circ }$. The sides AB and AC are equal. Using constructions, find which side of $\Delta ABC$ is the shortest.

1. BC

2. AC

3. AB

4. Data Insufficient

Q.

In Fig. T is a point on side QR of $\Delta PQR$ and S is a point such that RT = ST. Which of the following is true?

1. PQ + PR < QS

2. PQ + PR > QS

3. PQ + TR > QS

4. PQ + TR < QS

Q.

In the figure, sides QP and RQ of $\Delta$PQR are produced to points S and T, respectively. If $\angle$SPR = ${135}^{\circ }$ and $\angle$PQT = ${110}^{\circ }$, find 2$\angle$PRQ.

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

2. ${150}^{\circ }$

3. ${110}^{\circ }$

4. ${130}^{\circ }$

Q.

Consider the figure:

If BC = AC, x = 2y, and angle ACB = 60^o, then find the value of $\angle$A + $\angle$B + $\angle$x + $\angle$y (in degrees).

___

Q.

Find x.

1. ${17}^{\circ }$

2. ${14}^{\circ }$

3. ${27}^{\circ }$

4. ${24}^{\circ }$

Q. One of the angles of a triangle is ${130}^{\circ }$, and the other two angles are equal. What is the measure of each of these equal angles?

Q.

In the given figure, the value of 'x' and 'y' is:

1. $X={30}^{\circ },Y={55}^{\circ }$
2. $X={45}^{\circ },Y={75}^{\circ }$
3. $X={60}^{\circ },Y={75}^{\circ }$
4. $X={45}^{\circ },Y={30}^{\circ }$

Q. Two angles of a triangle are ${65}^{\circ }$ and ${45}^{\circ }$ then the third angle is:

1. ${70}^{\circ }$
2. ${75}^{\circ }$
3. ${60}^{\circ }$
4. ${80}^{\circ }$

Q.

The smallest angle in a triangle with angles in ratio 1:2:3 is

1. 60°

2. 30°

3. 15°

4. 45°