Question

The ratio of the measure of three angles of a triangle is 2:3:10. Find the measure of the largest angle.

Answer 1

Answer:

120 degrees

Step-by-step explanation:

Let the constant of proportionality between the angles of the given triangle be x.

Hence,

The Measure of The First Angle = 2x

The Measure of The Second Angle = 3x

The Measure of The Third Angle = 10x

The Angle Sum Property Of A Triangle says that the sum of all angles of any triangle is 180.

Hence,

$2x+3x+10x=180\\15x=180\\x=180/15\\x=12$

As the Constant Of Proportionality obtained is 12

Hence,

The Measure of The First Angle = 2*12 = 24

The Measure of The Second Angle = 3*12 = 36

The Measure of The Third Angle = 10*12 = 120

As The Third Angle is the largest, its measure is 120.

Answer 2

Answer:

The measure of the largest angle:

120°

Step-by-step explanation:

The sum of the internal angles of a triangle = 180°:

2 + 3 + 10 = 15

then:

180/15 = 12

then, the measure of the largest angle:

10 * 12 = 120°