Question

If the measure of AngleB is 40°, what measures can AngleA and AngleC be? Select all that apply.

20° and 30°
30° and 110°
55° and 85°
60° and 90°
70° and 70°

Answer 1

30º and 110º

55º and 85º

70º and 70º

Explanation:

got it right on edge. !

Answer 2

30° and 110°

55° and 85°

70° and 70°

Explanation:

Given that:

`\angle B = 90^\circ`

To find the possible values for the other two angles
`\angle A\ and\ \angle C`.

Property of a triangle is that the sum of all three angles is always equal to
`180^\circ`.

OR

`\angle A +\angle B +\angle C = 180^\circ\\\Rightarrow \angle A + 40^\circ + \angle C = 180^\circ\\\Rightarrow \angle A + \angle C = 180^\circ - 40^\circ\\\Rightarrow \angle A + \angle C = 140^\circ`

So, the sum of
`\angle A\ and\ \angle C` should be
`140^\circ`. We can select our answers according to this condition.

Option 1: 20° and 30°: the sum is
`50^\circ \\eq 140^\circ` hence, not correct.

Option 2: 30° and 110°: the sum is
`140^\circ` hence, correct.

Option 3: 55° and 85°: the sum is
`140^\circ` hence, correct.

Option 4: 60° and 90°: the sum is
`150^\circ \\eq 140^\circ` hence, not correct.

Option 5: 70° and 70°: the sum is
`140^\circ` hence, correct.

Hence, the possible answers can be:

30° and 110°

55° and 85°

70° and 70°