Question

if the measure of the angles of a triangle are represented by 2x, 3x - 15 , and 7x + 15, the triangle is

Answer 1

D An isosceles triangle

Step-by-step explanation:

Given that the angles of a triangle are represented by;

`\begin{gathered} 2x \\ 3x-15 \\ 7x+15 \end{gathered}`

Recall that the sum of angles in a triangles is equal to 180 degrees.

Summing up the given angles we have;

`\begin{gathered} (2x+3x-15+7x+15)^(\circ)=180^(\circ) \\ 2x+3x+7x-15+15=180 \\ 12x=180 \\ x=(180)/(12) \\ x=15 \end{gathered}`

We have calculated the value of x.

We now need to calculate the value of each angle;

`\begin{gathered} 2x=2(15)=30^(\circ) \\ 3x-15=3(15)-15=30^(\circ) \\ 7x+15=7(15)+15=120^(\circ) \end{gathered}`

Therefore, the angles of the triangle are;

`30^(\circ),30^(\circ),120^(\circ)`

From the derived angles, we can notice that the triangle has two equal angles.

So it is an Isosceles triangle.