Angle Sum Property

Q.

Show that :$\mathrm{Cos}{24}^{°}+\mathrm{Cos}{55}^{°}+\mathrm{Cos}{125}^{°}+\mathrm{Cos}{204}^{°}+\mathrm{Cos}{300}^{°}=\frac{1}{2}$

Q.

What is the sum of three angles in a triangle?

Q.

Prove that the diagonals of a rectangle bisect each other. [4 MARKS]

Q.

A triangle can have at the most ____ right angle(s).

1. 2
2. 1
3. 3
4. 4

Q.

If $z=\log \left(\tan x+\tan y\right)$, then $\sin 2x·\left(\frac{\partial z}{\partial x}\right)+\sin 2y·\left(\frac{\partial z}{\partial y}\right)$ is equal to

1. $1$

2. $2$

3. $3$

4. $4$

Q.

If angles of a triangle are in the ratio 2:3:5, then find the smallest angle.

1. ${26}^{\circ }$

2. ${46}^{\circ }$

3. ${40}^{\circ }$

4. ${36}^{\circ }$

Q.

Of the three angles of a triangle one is twice the smallest and another is twice the smallest and another is three times the smallest . Find the angles.

Q.

In a triangle $ABC,$ the value of $\sin \left(2A\right)+\sin \left(2B\right)+\sin \left(2C\right)$ is equal to:

1. $4\sin \left(A\right)\sin \left(B\right)\sin \left(C\right)$

2. $4\cos \left(A\right)\cos \left(B\right)\cos \left(C\right)$

3. $2\cos \left(A\right)\cos \left(B\right)\cos \left(C\right)$

4. $2\sin \left(A\right)\sin \left(B\right)\sin \left(C\right)$

Q.

The vertical angle of an isosceles triangle is twice the sum of its base angles. Find each of the angle of the triangle.

Q.

The angles of a triangle are in the ratio $3:5:10$. Find the measure of each angle of the triangle.

Q.

If the pair of straight lines given by $A{x}^2+2Hxy+B{y}^2=0,(H^2>AB)$ forms an equilateral triangle with line $ax+by+c=0$, then $(A+3B)(3A+B)$ is

1. $H^2$

2. $-H^2$

3. $2H^2$

4. $4H^2$

Q.

If$A,B,C$ are angles of a triangle, then $\sin 2A+\sin 2B-\sin 2C$ is equal to

1. $4\sin A\cos BcosC$

2. $4\cos A$

3. $4\sin A\cos A$

4. $4\cos A\cos B\sin C$

Q. The sum of four angles of a quadrilateral is _____.

1. 90°
2. 180°
3. 270°
4. 360°

Q.

In a triangle $ABC$, angle $A$ $-$ angle $B$ $=15$ degrees and angle $B$ - angle $C$ $=30$ degrees. Find angles $A,B$ and $C$.

Q.

If two angles of $∆\mathrm{ABC}$ are ${45}^{°}$ and ${60}^{°}$, then the ratio of the smallest and the greatest sides are

Q.

In the given figure, find the value of $\angle \text{A}+\angle \text{B}+\angle \text{C}+\angle \text{D}+\angle \text{E}+\angle \text{F}$.

1. 1 right angle

2. 2 right angles

3. 3 right angles

4. 4 right angles

Q.

The _____ triangle always has altitude outside itself.

Q.

It is possible for an obtuse triangle to be isosceles.

1. True
2. False

Q.

The sum of all three interior angles in a right angled triangle is equal to ___.

1. ${360}^{\circ }$

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

3. ${240}^{\circ }$

4. ${180}^{\circ }$

Q.

The three angles are in ratio $2:3:5$. find the measure of each angle. classify the triangle

Q.

The ratio between the base angle and the vertical angle is 2:5 find each angle of the triangle

Q.

The value of $\underset{x\to 0}{\lim }{\left(\cos \left(x\right)\right)}^{{\cot }^2\left(x\right)}$ is

1. $e^{-1}$

2. $e^{-\frac{1}{2}}$

3. $1$

4. Does not exist.

Q.

One angle of a quadrilateral is of$108°$and the remaining three angles are equal. Find each of the three equal angles.

Q.

All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

Q.

One side of a triangle is produced and the exterior angle so formed is 140°. If the corresponding interior opposite angles are in the ratio 3:4, find the measure of all the angles of the triangle.

Q.

In the given isosceles triangle ABC, AB = AC, $\angle ABC$ = 70°. Find $\angle$ BAC.

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

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

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

4. ${50}^{\circ }$

Q.

Angles of a triangle are $(x+{10}^{\circ }),(x+{40}^{\circ })$ and $(2x-{30}^{\circ })$. Find the value of x.

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

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

3. ${20}^{\circ }$

4. ${10}^{\circ }$

Q. In a triangle ABC it is given that angle B is 37 degrees and angle C is 29 degrees then what is the measure of angle A?

Q. If two angles of a quadrilateral are of measure 75${}^{\circ }$ and the other two angles are equal, then the measure of the angle is

1. 105${}^{\circ }$
2. 110${}^{\circ }$
3. 120${}^{\circ }$
4. 130${}^{\circ }$

Q.

Question 77

The sum of two vertically opposite angles is ${166}^{\circ }$. Find each of the angles.