Triangle and Sum of Its Internal Angles

Q.

Prove that the sum of angles of a triangle is $180°$.

Q.

In the given figure, $BO$ and $CO$ are the bisectors of $\angle B$ and $\angle C$ respectively. If $\angle A={50}^{\circ }$ then $\angle BOC=?$

$\left(a\right){130}^{\circ }\left(b\right){100}^{\circ }\left(c\right){115}^{\circ }\left(d\right){120}^{\circ }$

Q.

The sum of two angles of a triangle is equal to its third angle . Determine he measure of the third angle .

Q.

If two acute angles of a right triangle are equal, then each acute is equal to:

Q.

In the given figure, AB || PQ. Find the values of x and y.

Q.

In a $\Delta ABC,$ if $\angle A={60}^{\circ },\angle B={80}^{\circ }$ and the bisectors of $\angle B$ and $\angle C$ meet at $O$, then $\angle BOC=$___

Q.

If all the three angles of a triangle are equal, then each one of them is equal to

Q.

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

Q.

In $\Delta RST$ (in the figure), what is the value of x?

Q.

In a right -angled triangle, one of the acute angles measures ${53}^{\circ }$ .Find the measure of each angle of the triangle.

Q.

ABC is a triangle in which $\angle A={72}^{\circ }$, the internal bisectors of angles B and C meet in O. Find the magnitude of $\angle BOC$.

Q.

In a triangle ABC if angle A + angle B = 65 degrees and angle B + angle C = 140 degrees, calculate angle A and angle B

Q.

In the given figure, m and n are two plane mirrors perpendicular to each other. Show that the incident ray CA is parallel to the reflected ray BD.

Q.

The bisects of exterior angles at B and C of $\Delta ABC$, meet at O. If $\angle A=x^{\circ }$, then $\angle BOC$=

Q.

In a $\Delta ABC,$ $D$ is the midpoint of side $AC$ such that $BD=\frac{1}{2}AC.$ Show that $\angle ABC$ is a right angle.

Q.

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

Q.

Calculate the value of x in each of the following figures.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Q.

The angle of a triangle are $3x,2x-7$ and $4x-11.$ Then, the value of $x$ is?

Q.

In $\Delta ABC,$ if bisectors of $\angle ABC$ and $\angle ACB$ intersect at O at angle of ${120}^{\circ }$ , then find the measure of $\angle A.$

Q. If A, B, C are three angles of triangle. If A -B=15. B-C=30. Find A , B, C.

Q. In the given figure, what type of a triangle is $△ABC$, provided DB = AB and AC = CE?

1. Equilateral
2. Scalene
3. Right-angled
4. Isosceles

Q.

In $\Delta ABC$, if $\angle A+\angle B={125}^{\circ }$ and $\angle A+\angle C={113}^{\circ }$, find $\angle A,\angle B$ and $\angle C$.

Q.

Angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is

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

2. 30${}^{\circ }$

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

4. 80${}^{\circ }$

Q. The exterior angles obtained on producing the base of a triangleABC both ways are 100degree and 120degree. Find all the angles of the triangle.

Q. Question 8
The angles of a triangle are in the ratio 2 : 3 : 4. Find the angles of the triangle.

Q.

$In\Delta ABC,if\angle A+\angle B={108}^{\circ }and\angle B+\angle C={130}^{\circ },find\angle A,\angle Band\angle C.$

Q.

In the figure, AM $\perp$ BC and AN is the bisector of $\angle A$. If $\angle B$=${65}^{\circ }$ and $\angle C={33}^{\circ }$, find $\angle MAN.$

Q.

Write the sum of the angles of an obtuse triangle.

Q.

If one of the angles of a triangle is ${130}^{\circ }$ then the angle between the bisectors of the other two angles can be

(a) ${50}^{\circ }$

(b) ${65}^{\circ }$

(c) ${90}^{\circ }$

(d) ${155}^{\circ }$

Q.

$\text{In the given figure, two rays BD and CE intersect at a point A . The side BC of}\Delta ABC\text{have been produced on both sided to points F and G respectively .If}\angle ABF=x^{\circ },\angle ACG=y^{\circ }and\angle DAE=z^{\circ }Thenz=?$

$\left(a\right)x+y-180\left(b\right)x+y+180\left(c\right)180-(x+y)\left(d\right)x+y+{360}^{\circ }$