Answer:

a. Find the sum of ratios:

1+2+3 = 6

Divide to the internal angle (180)

180/6 = 30

Multiply to the ratios

1*30 = 30 degrees

2*30 = 60 degrees

3*30 = 90 degrees

ANSWER: The measure of angles are 30,60, and 90 degrees

b. Find the sum of ratio

2+5+6 = 13

Divide to the perimeter

65/13 = 5

Multiply to the ratios

2*5 = 10 cm

5*5 = 25 cm

6*5 = 30 cm

ANSWER: The measure of sides are 10,25,30 cm

Answer:

a. The measure of all the angles of a triangle = 180°

1x + 2x + 3x = 180°

6x = 180°

6x/6 = 180°/6

x = 30

Angle 1 = 30 * 1 = 30°

Angle 2 = 30 * 2 = 60°

Angle 3 = 30 * 3 = 90°

30° + 60° + 90° = 180°,

It is proved that 30°, 60°, 90° are the three measures of the three angles of the triangle.

b. Perimeter = 65cm

Ratio of sides = 2:5:6

So, let us add the numbers to know the total number: 2 + 5 + 6 = 13

the ratio of the sides is:  2/13, 5/13 and 6/13

2/13 × 65 = 130/13 = 10

5/13 × 65 = 325/13 = 25

6/13 × 65 = 390/13 = 30

10 + 25 = 35 + 30 = 65