R. D. Sharma Solutions for Chapter: Triangle and its Angles, Exercise 1: EXERCISE

In $△ABC$, $\angle A=55°$ and $\angle B=40°$. Find $\angle C$.

The angles of a triangle are $(x-40)°, (x-20)°$and $\left(\frac{1}{2}x-10\right)°$. Find the value of $x$.

The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is $10°,$ find the three angles.

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

The bisectors of base angles of a triangle cannot enclose a right angle in any case.

If the bisectors of the base angles of a triangle enclose an angle of $135°$, prove that the triangle is a right triangle.

In a $△ABC, \angle ABC=\angle ACB$ and the bisectors of $\angle ABC$ and $\angle ACB$  intersect at $O$ such that $\angle BOC=120°.$ Show that $\angle A=\angle B=\angle C=60°.$

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