Answer:
30° and 110°
55° and 85°
70° and 70°
Step-by-step explanation:
Given that:
[tex]\angle B = 90^\circ[/tex]
To find the possible values for the other two angles [tex]\angle A\ and\ \angle C[/tex].
Property of a triangle is that the sum of all three angles is always equal to [tex]180^\circ[/tex].
OR
[tex]\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[/tex]
So, the sum of [tex]\angle A\ and\ \angle C[/tex] should be [tex]140^\circ[/tex]. We can select our answers according to this condition.
Option 1: 20° and 30°: the sum is [tex]50^\circ \neq 140^\circ[/tex] hence, not correct.
Option 2: 30° and 110°: the sum is [tex]140^\circ[/tex] hence, correct.
Option 3: 55° and 85°: the sum is [tex]140^\circ[/tex] hence, correct.
Option 4: 60° and 90°: the sum is [tex]150^\circ \neq 140^\circ[/tex] hence, not correct.
Option 5: 70° and 70°: the sum is [tex]140^\circ[/tex] hence, correct.
Hence, the possible answers can be:
30° and 110°
55° and 85°
70° and 70°
