Question

10. Write an inequality relating the measure of angle 1 to the measure of angle 2

Answer 1

The inequality relating the measure of angle 1 to the measure of angle 2 is ∠2 > ∠1.

How to write the inequality relating angle 1 and angle 2?

The inequality relating the measure of angle 1 to the measure of angle 2 is determined as follows;

The measure of angle 1 is calculated by applying cosine rule;

5² = 6² + 6² - (2 x 6 x 6) cos(∠1)

25 = 72 - 72 cos∠1

72 cos∠1 = 72 - 25

72 cos∠1 = 47

cos∠1 = 47 / 72

cos∠1 = 0.6528

∠1 = arc cos (0.6528)

∠1 = 49.2⁰

The measure of angle 1 is calculated by applying cosine rule;

9² = 6² + 6² - (2 x 6 x 6) cos(∠2)

81 = 72 - 72 cos∠2

72 cos∠2 = 72 - 81

72 cos∠2 = -9

cos∠2 = - 9 / 72

cos∠2 = -0.125

∠2 = arc cos (-0.125)

∠2 = 97.2⁰

So the inequality becomes ∠2 > ∠1 (angle 2 is greater than angle 1)

Answer 2

The two triangles are isosceles.

Both triangles have the equals sides equal to 6

Both ∠ 1 and the ∠2 are the opposite angles to the different side of their respective triangles.

The opposite side to ∠ 1 is shorter than the opposite side to ∠ 2, which implies that ∠1 is less than ∠2.

Then the inequality that relates those angles is

∠1 < ∠2