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

Answer:

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

Step-by-step 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°.