Q.

If the sides of a triangle are produced in order, prove that the sum of the exterior angles so formed is equal to four right angles.

Q. In $△ABC$, if $\angle B={76}^{\circ }$ and $\angle C={48}^{\circ }$, find $\angle A$ (in degrees).

Q. In a $△ABC$, if $3\angle A=4\angle B=6\angle C$, calculate the angles.

Q. Of the three angles of a triangle one is twice the smallest and another is thrice the smallest. Find the largest angle in degrees

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

Q. In the given fig $AD$ divides $\angle BAC$ in the ratio $1:3$ and $AD=DB$. Determine 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. In the given figure, the side $BC$ of $△ABC$ has been produced on the left-hand side from $B$ to $D$ and on the right -hand side from $C$ to $E$. if $\angle ABD={106}^{\circ }$ and $\angle ACE={118}^{\circ }$, find the measure of each angle of the triangle.

Q. $AM\perp BC$ and $AN$ is the bisector of $\angle A$. If $\angle ABC={70}^{\circ }$ and $\angle ACB={20}^{\circ }$ find the value of $\angle MAN$

Q. If one angle of a triangle is less then the sum of the other two, show that the triangle is acute angled.

Q. In the figure, show that $\angle A+\angle B+\angle C+\angle D+\angle E+\angle F={360}^{\circ }$.

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

Q. In the given figure, side $$BC$$ of $$\triangle ABC$$ is produced to $$D$$. If $$\angle ACD = 128^{\circ}$$, and $$\angle ABC = 43^{\circ}$$, find $$\angle BAC$$ and $$\angle ACB$$.

Q. If one angle of a triangle is greater than the sum of the other two, show that the triangle is obtuse angled.

Q. If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle.

Q. In $$\triangle PQR$$, if $$\angle P - \angle Q = 42^{\circ}$$ and $$\angle Q - \angle R = 21^{\circ}$$, find $$\angle P, \angle Q$$ and $$\angle R$$.

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

Q. The sum of two angles of a triangle is ${116}^{\circ }$ and their difference is ${24}^{\circ }$ Find the measure of each angle of the triangle.

Q. Two angles of a triangle are equal and the third angle is greater than each one of them by ${18}^{\circ }$. Find the angles.

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