High School

A triangle has one angle that measures five degrees more than twice the smallest angle. Also, the largest angle

measures eleven degrees less than three times the measure of the smallest angle. Find the measures of all three

angles.

A triangle has one angle that measures five degrees more than twice the smallest angle Also the largest angle measures eleven degrees less than three

Answer :

Answer:

The smallest angle = 31⁰

The second angle = 67⁰

The largest angle = 82⁰

Step-by-step explanation:

Let the smallest angle be x, the second angle is 2x + 5 and the largest angle is 3x - 11.

x + 2x + 5 + 3x - 11 = 180⁰ (sum of angles in a triangle)

6x + 5⁰ - 11⁰ = 180⁰

6x - 6⁰ = 180⁰

6x = 180⁰ + 6⁰

6x = 186 Divide both sides by 6

x = 186 / 6

x = 31⁰

The smallest angle = 31⁰

The second angle = 2x + 5⁰

= 2(31⁰) + 5⁰

= 62⁰ + 5⁰

= 67⁰

The largest angle = 3x - 11

= 3(31⁰) - 11

= 93⁰ - 11⁰

= 82⁰

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