Question

A marble path, as shown at the right, is constructed out of several congruent isosceles triangles. All the vertex angles measure 20°. What is the measure of angle 1 in the figure?

Answer 1

The measure of the angle 1 for the figure is equal to 80 degrees.

The measure of the angle 1 can be calculated by first finding the sum of the angles on the marble part that share the same point with the angle 1 and then subtracting the result from 360° as follows:

Let one base angle of the Isosceles triangle be x so that we have

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 160/2

x = 80

Since the angle 1 share same point with 6 vertices and two base angles on the marble thus;

angle 1 = 360 - [6(20) + 2(80)]

angle 1 = 360 - 280

angle 1 = 80°

Therefore, we have that measure of the angle 1 derived to be 80 degrees.