Question

the ratio of the measure of one angle of an equilateral triangle to the sum of all its angles

Answer 1

$\huge{\mathcal{\boxed{\blue{Solution}}}}$

We know that all angles of an equilateral triangle is 60

The one angle is 60

and the sum of all angles is

60+60+60=180

The ratio is

➡60/180

➡1:3

Answer 2

Given,

The equilateral triangle is given.

To find,

We have to find the ratio of the measure of one angle of an equilateral triangle to the sum of all its angles.

Solution,

The ratio of the measure of one angle of an equilateral triangle to the sum of all its angles is 1:3.

We can simply find the ratio of the measure of one angle of an equilateral triangle to the sum of all its angles by using the fact that all the sides and angles of the equilateral triangle are equal.

Let A, B, and, C be the three angles of the equilateral triangles such that ∠A = 60°, ∠B = 60°, and ∠C = 60°.  

We know that by Angle Sum Property the sum of all the angles of a triangle is 180°.

⇒ ∠A +∠B+∠C = 180°

Required ratio = ∠A / ∠A +∠B+∠C

                        = 60/180

                         = 1/3

Hence, the ratio of the measure of one angle of an equilateral triangle to the sum of all its angles is 1:3.