Triangle and Sum of Its Internal Angles

Q.

In the given figure, O is the centre of a circle, BOA is its diameter and the tangent at the point P meets BA extended at T. If $\angle$ PBO = ${30}^o$ then $\angle$ PTA = ?

(a) ${60}^o$ (b) ${30}^o$ (c) ${15}^o$ (d) ${45}^o$

Q.

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

1. ${90}^{\circ }+\frac{1}{2}\angle A$

2. ${90}^{\circ }+\frac{1}{2}\angle B$

3. ${90}^{\circ }+\frac{1}{2}\angle C$

4. ${90}^{\circ }-\frac{1}{2}\angle A$

Q. In figure $\angle QPR={90}^{\circ },PS$ is its bisector.
If $ST\perp PR$, prove that $ST\times (PQ+PR)=PQ\times PR$.

Q. In ΔABC, D, E and F are points on AB, AC and BC respectively. If AD : DB : EF = 3 : 2 : 2 and DE : BC = 3 : 5, then which of the following option is correct?

ΔABC में बिन्दु D, E व F क्रमशः AB, AC व BC पर हैं। यदि AD : DB : EF = 3 : 2 : 2 तथा DE : BC = 3 : 5 है, तब निम्नलिखित में से कौनसा विकल्प सही है?

1. DF || AC
2. CF : BF = 3 : 2
3. EF : AB = 3 : 5
4. EF || AB

Q. O is the centre of the circle and BCD is the tangent to it at C. $\angle BAC+\angle ACD$=

1. 180
2. 90
3. 60
4. 150

Q. In a triangle $ABC,\cos 3A+\cos 3B+\cos 3C=1$, then find any one angle.

Q. In $∆ABC,\angle A=x^{\circ },\angle B={\left(3x-2\right)}^{\circ },\angle C=y^{\circ }\mathrm{and}\angle C-\angle B=9^{\circ }.$ Find the three angles.

Q. If the ratio of the angles of a triangle are in the ratio $3:4:5$, then its angles (in degrees) are

1. 48, 52, 80
2. 45, 60, 75
3. 45, 75, 90
4. 45, 65, 70

Q. In the given figure, $AD$ bisects $\angle A$. If $\angle B={60}^0$, $\angle C={40}^0$, then arrange $AB$, $BD$ and $DC$ in ascending order of their lengths.

1. $BC>DC>AB$
2. $BC<DC<AB$
3. $BC>AB>DC$
4. $BC<AB<DC$

Q. The given figure shows a right triangle right angled at B If $\angle BCA=2\angle BAC,$ Then, $\frac{AC}{BC}=$

Q. In the adjoining figure, the sides $AB$ and $AC$ of $\Delta ABC$ are produced to $D$ and $E$ respectively. If bisector of $\angle CBD$ and $\angle BCE$ meet at $O$, then show that $\angle BOC={90}^o-\frac{\angle A}{2}$.

Q. In the figure , $\angle BAD=3\angle DBA$ , find $\angle ABC$ (in degrees)

Q. Macy is dressed as a geometric shape for Halloween. She came up with a riddle to introduce herself to her friends.
She says, "I am a plane figure with three sides, and the sum of two of my angles is 90°".

What is Macy's costume?

Q.

In $\Delta ABC,AB=7.6cm,BC=6.9cm$ and $CA=6.1cm.$

The greatest angle is:

1. $\angle C$
2. $\angle B$
3. none of these
4. $\angle A$