Maharashtra Board Solutions for Chapter: Triangles, Exercise 1: Practice set 3.1

In $∆\mathrm{PQR}$, $\angle P=70°$, $\angle Q=65°$ then $\angle R$ is $k°$. Find the value of $k$.

The measures of angles of a triangle are $x°,\left(x-20\right)°,\left(x-40\right)°$. Find the measure of each angle.

The measure of one of the angles of a triangle is twice the measure of its smallest angle and the measure of the other is thrice the measure of the smallest angle. The measures of the three angles is $k°, 60°, 90°$. Find the value of $k$.

In figure, measures of some angles are given. Find the measure of $x$ (Write the answer without degree symbol).

In figure, line $AB \parallel$ line $DE$. Find the measure of $\angle ARE$ ( in degrees) using given measures of some angles.

In $△ABC$, bisectors of $\angle A$ and $\angle B$ intersect at point $O$. If $\angle C=70°$. The measure of $\angle AOB$ is $k°$. Find the value of $k$.

Using the information in figure, find the measures of $\angle a, \angle b$ and $\angle c$.

In figure, line $\mathrm{DE} \parallel$ line $\mathrm{GF}$ and ray $\mathrm{EG}$ and ray $\mathrm{FG}$ are bisectors of $\angle \mathrm{DEF}$ and $\angle \mathrm{DFM}$ respectively.

Prove that, $\mathrm{EF}=\mathrm{FG}$