Properties of the Angles of a Triangle

In the given figure, $\mathrm{p}\parallel \mathrm{q}$. Find the value of $\mathrm{x}$.

In the given figure, $\mathrm{p}\parallel \mathrm{q}$. Find the value of $\mathrm{x}, \mathrm{y}, \mathrm{z}.$

In the given figure AC, AD and AE are joined. Prove that $\angle \mathrm{FAB}+\angle \mathrm{ABC}+\angle \mathrm{BCD}+\angle \mathrm{CDE}+\angle \mathrm{DEF}+\angle \mathrm{EFA}={720}^{°}$.

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.

Is it possible to have a triangle in which two of the angles are acute.

Is it possible to have a triangle in which two of the angles are obtuse.

Is it possible to have a triangle in which two of the angles are right angles.

Is it possible to have a triangle in which each angle is equal to ${60}^{°}$.

Is it possible to have a triangle in which each angle is equal to ${45}^{°}$.

Find the value of $\mathrm{x}$.

In the given figure, find the value of $x$.

In the given figure, find the value of $x$.

In the given figure, find the value of $x$.

In the given figure, find the value of $x$.

In the given figure, find the value of $x$.

In $△\mathrm{ABC}$, if $3\angle \mathrm{A}=6\angle \mathrm{B}=8\angle \mathrm{C},$ calculate the measures of $\angle \mathrm{A}, \angle \mathrm{B}$ and $\angle \mathrm{C}$.

In a triangle ABC, $\angle \mathrm{A}-\angle \mathrm{B}={15}^{°} \mathrm{and} \angle \mathrm{B}-\angle \mathrm{C}={30}^{°}$. Find the measure of each angle of the triangle.

In an isosceles triangle ABC, the measure of vertex angle A is ${30}^{°}$ more than the measure of each angle of each base angle. Find the measure of each angle of the triangle.

The acute angles of a right triangle are in the ratio of $4:5$. Find each of these angles.

If one acute angle of a right triangle is half of the other, find the measure of both acute angles.