Question

if the measure of angle A of triangle ABC is 5x+10, the measure of angle N is x+10, and the measure of angle C is 2x, which of the following is true of triangle ABC? a. Triangle ABC is acute and scalene b. Triangle ABC is acute but not scalene c. Triangle ABC is right but no isosceles d. Triangle ABC is obtuse but not scalene e. Triangle ABC is acute and scalene

Answer 1

Given the expressions for the angles in triangle ABC, we can solve for x, substitute back into the expressions to find the actual angle measurements, and conclude that the triangle is acute and scalene.

Step-by-step explanation:

The subject of this problem is geometry, specifically triangle properties. In a triangle, the sum of the measures of the three angles is always 180 degrees. Given that Angle A = 5x+10, Angle N = x+10, and Angle C = 2x, we can set up an equation to solve for x:

5x + 10 + x + 10 + 2x = 180, which simplifies to 8x + 20 = 180, then 8x = 160, and finally x = 20.

Substituting x = 20 back into the original angle measurements gives: Angle A = 110 degrees, Angle N = 30 degrees, and Angle C = 40 degrees. Since all these angles are less than 90 degrees, the triangle is acute. Also, as all the angles (and thus, the sides opposite them) are different, the triangle is scalene. So, the answer is 'Triangle ABC is acute and scalene'.

Learn more about Triangle Properties