Question

In a triangle, measure of one angle is 60º. The measure of one of the remaining two angles is twice the other. Find the measure of the smallest angle of the triangle.

a. 60º
b. 40º
c. 120º
d. 80º

Answer 1

Answer:

So, the measure of the smallest angle of the triangle is $40^{0}$.  

Option (b) $40^{0}$ is correct.  

Step-by-step explanation:

In context to question asked,

• We have to find the measure of the smallest angle of the triangle.
• It is given that, measure of one angle = 60º.
• The measure of one of the remaining two angles is twice the other.
• Let, one angle be $x$ and other angle be $2x$.
• Now, we know that, the sum of angles of a triangle is $180^{0}$.
• So, the required equation is,

       $x+2x+60=180$

          ∴ $3x+60=180$

                 ∴ $3x=180-60$

                 ∴ $3x=120$

                  ∴ $x=\frac{120}{3}$

                  ∴ $x=40^{0}$

• And $2x=2\times40=80^{0}$

• So, the measure of the smallest angle of the triangle is $40^{0}$.    

      Option (b) $40^{0}$ is correct.  

Answer 2

Answer:

The measure of the smallest angle is 40 degree

Step-by-step explanation:

Given:

Measure of one angle = 60 degree

Here it is given that the measure of one of the remaining two angle is twice the other.

Let smaller angle =X degree

So, the remaining angle = 2X

As we know that

The sum of all the angles of a triangle is equal to 180 degree

So,

60 + X + 2X = 180

60 + 3X =180

       3X =180 - 60

          X =120 /3

          X = 40

∴ The measure of smallest angle = X =40 degree