Question

The measure of the smallest angle of a triangle is one-third the measure of the largest
angle. The measure of the second angle is 65° less than the measure of the largest
angle. Find the measure of the angles of the triangle.

Answer 1

The biggest angle is 105°, the smallest angle is  35° and the second angle is 40°

A triangle is a polygon that has three sides and three angles. The sum of angles is a triangle is 180 degrees.

Types of triangles

• Right angled triangle
• Isosceles triangle
• Equilateral triangle
• Scalene triangle

From the question, the following information was derived:

• smallest angle = $\frac{1}{3}$x
• second angle = x - 65
• largest angle is represented with x

$\frac{1}{3}$x + (x - 65 ) + x = 180

Combine similar terms

$\frac{1}{3}$x + x + x = 180 + 65

Add similar terms together

$\frac{7}{3}$x = 245

Divide both sides of the equation by 3/7

x = 105

The biggest angle  is 105°

smallest angle =  $\frac{1}{3}$ x 105 = 35°

Second angle = 105 - 65 = 40°

In order to determine the value of each angle, determine the value of the largest angle first and then use the the value to determine the value of the other angles

A similar question was solved here: https://brainly.com/question/22240750?referrer=searchResults