Question

A. What do you notice about each exterior angle measurement when you arrange the triangles so that the three angles form a straight line?

B. If angle 1 = 60o and angle 2 = 90o, what is the measurement of angle 3?

C. If angle 1 = 60o and angle 2 = 90o, what is the sum of angles 1 and 2?

D. What do you notice about the sum of the angles inside the triangle and the exterior angle measurement?

Answer 1

The sum of angles inside a triangle is the sum of angles 1, 2 and 3, which form a straight line, therefore 180 degrees.

The sum of the exterior angles
angle exterior angle
1 2+3
2 1+3
3 1+2
total 2+3+1+3+1+2=2(1+2+3)=2(180)=360 degrees.

Answer 2

We are given with figure of Right angled triangle.

m∠2 = 90°

A).

When we arranged the triangles so that the three angles form a straight line.

We notice that,

Measure of the exterior angle of ∠1 = ∠2 + ∠3

Measure of the exterior angle of ∠2 = ∠1 + ∠3

Measure of the exterior angle of ∠3 = ∠1 + ∠2

B).

If, m∠1 = 60° and m∠2 = 90°

To find: m∠3

From Figure,

∠3 + ∠2 + ∠1 = 180° ( linear pair angles )

∠3 + 90 + 60 = 180

∠3 = 180 - 150

∠3 = 30°

C).

If, m∠1 = 60° and m∠2 = 90°

Sum of both angles = 60 + 90 = 150°

D).

Sum of the interior angle and Exterior angles

= ∠1 + ∠2 + ∠3 + (∠2 + ∠3) + (∠1 + ∠3) + (∠1 + ∠2)

= 2 ∠1 + 2 ∠2 + 2 ∠3

= 2 ( ∠1 + ∠2 + ∠3 )

= 2 × 180

= 360°