Question

The angles of a triangle are $$2x$$, $$3x$$, and $$4x$$ degrees. What is the value of $$x$$?

Answer 1

Hint: Given the angles of a triangle are $$2x$$, $$3x$$, and $$4x$$ degrees. As we know, the sum of the measure of all the three angles in a triangle is $$180$$ degrees. So, in this question, we will sum up all the three measures of the angle of the triangle and equate it to $$180$$ degrees i.e., $$2x+3x+4x=180$$ and then we will simplify it to find the value of $$x$$.

Complete step by step answer:
Given the angles of a triangle are $$2x$$, $$3x$$ and $$4x$$ degrees, we have to find the value of $$x$$.

As we know, the sum of the measure of all the three angles in a triangle is $$180$$ degrees.
On adding all the three measures of the angle of the triangle and equating it to $$180$$ degrees, we get
$$\Rightarrow 2x+3x+4x=180$$
On simplification, we get
$$\Rightarrow 9x=180$$
On dividing both the sides of the equation by $$9$$, we get
$$\Rightarrow x={\displaystyle \frac{180}{9}}$$
On calculating, we get
$$\Rightarrow x=20$$
Therefore, the value of $$x$$ is $$20$$.

Note:
Here, the question is of a triangle. Like the sum of the measures of the angles of a triangle having three sides is always $${180}^{\circ }$$. Similarly, the sum of the measure of the angles of a quadrilateral having four sides is always $${360}^{\circ }$$, the sum of the measure of the angles of a pentagon having five sides is always $${540}^{\circ }$$ and the sum of the measure of the angles of a hexagon having six sides is always $${720}^{\circ }$$.