Identify the Triangle Type: Analysis of 60° Angle Properties

Question

Identify which type of triangle appears in the drawing:

606060

Video Solution

Solution Steps

00:00 Determine what type of triangle is shown in the drawing
00:03 The sum of the angles in a triangle equals 180
00:06 Apply this equation and proceed to solve for A
00:15 Isolate A
00:31 This is the value of A
00:34 Substitute in this value and determine the triangle's angles
00:38 Based on the angles, the triangle is acute
00:42 This is the solution

Step-by-Step Solution

Note that the sum of angles in a triangle equals 180 degrees.

Let's calculate alpha in the following way:

60+α+α2=180 60+\alpha+\frac{\alpha}{2}=180

60+112α=180 60+1\frac{1}{2}\alpha=180

112α=18060 1\frac{1}{2}\alpha=180-60

112α=120 1\frac{1}{2}\alpha=120

Let's divide both sides by 1.5:

α=80 \alpha=80

Now we can calculate the remaining angle in the triangle:

α2=802=40 \frac{\alpha}{2}=\frac{80}{2}=40

So in the triangle we have 3 angles: 60, 80, 40

All of them are less than 90 degrees, therefore all angles are acute angles and the triangle is an acute triangle.

Answer

Acute triangle