Question

One angle of an isosceles triangle measures 30°. Which other angles could be in that isosceles triangle? Choose all that apply.

a-30
b-120
c-35
d-75

Answer 1

a or d) Other angle that could be in that isosceles triangle is 75°or 30°.

Explanation:

Let us assume the given isosceles triangle is ABC.

Now, In an ISOSCELES TRIANGLE, two sides are equal.

⇒ AB = AC

CASE - 1 : Here: ∠A = 30°

Now,a s we know: ANGLES OPPOSITE TO EQUAL SIDES ARE EQUAL.

Now, as AB = AC

⇒ ∠B = ∠C = x

Now, by ANGLE SUM PROPERTY:

∠A + ∠B + ∠C = 180°

or, 30° + x + x = 180

or, 2 x = 150

or, x = 150/2 = 75

⇒ ∠B = ∠C = 75°

Case 2: ∠B = 30°

So, ∠C = 30°

Hence, other angles that could be in that isosceles triangle is 75° or 30°.