Jagat Jitendra Matto Solutions for Chapter: The Triangle and Its Properties, Exercise 1: EXERCISE 12.1

In the given figure, $∆\mathrm{ACB}$ is a right angled triangle at $\mathrm{C}$ and $\mathrm{CD}\perp \mathrm{AB}$. If $\angle \mathrm{B}= {40}^{°}$, then find: $\angle \mathrm{BAC}$

In the given figure, $∆\mathrm{ACB}$ is a right angled triangle at $\mathrm{C}$ and $\mathrm{CD}\perp \mathrm{AB}$. If $\angle \mathrm{B}={40}^{°}$, then find $\angle \mathrm{ACD}$

In the given figure, $∆\mathrm{ACB}$ is a right angled triangle at $\mathrm{C}$ and $\mathrm{CD}\perp \mathrm{AB}$. If $\angle \mathrm{B}= {40}^{°}$, then find $\angle \mathrm{BCD}$.

Two acute angles of a right angled triangle are equal. Find the two angles.

In the given five sided closed figure, find $\angle \mathrm{EAB}+\angle \mathrm{ABC}+\angle \mathrm{BCD}+\angle \mathrm{CDE}+\angle \mathrm{DEA}$

The angles of a triangle are in the ratio $5: 4: 3$. Find the measure of each angle.

In $∆\mathrm{ABC}, 2\angle \mathrm{A}=3\angle \mathrm{B}=6\angle \mathrm{C}$. Calculate $\angle \mathrm{A}, \angle \mathrm{B}$ and $\angle \mathrm{C}$.

[Hint: $2\angle \mathrm{A}=3\angle \mathrm{B}\Rightarrow \angle \mathrm{A}:\angle \mathrm{B}=3:2 \text{and} 3\angle \mathrm{B}=6\angle \mathrm{C}\Rightarrow \angle \mathrm{B}:\angle \mathrm{C}=6:3=2:1 \text{thus}, \angle \mathrm{A}:\angle \mathrm{B}:\angle \mathrm{C}=3:2:1$]

The angles of a triangle are $(x+21{)}^{°}, x^{°}$ and $(2x-45{)}^{°}$. Find the value of $x$.