1) One angle of an isosceles triangle measures $$ 100^{\circ} $$. What measures are possible for the other two angles? Choose all that apply.

Question

UpStudy AI · Accepted Answer

In an isosceles triangle, two angles are equal. Given that one angle measures $$ 100^{\circ} $$, we can denote the angles of the triangle as follows:

- Let $$ A = 100^{\circ} $$ (the given angle).
- Let $$ B $$ and $$ C $$ be the other two angles, which are equal since the triangle is isosceles.

The sum of the angles in any triangle is $$ 180^{\circ} $$. Therefore, we can write the equation:

$$
A + B + C = 180^{\circ}
$$

Substituting $$ A $$ into the equation gives:

$$
100^{\circ} + B + B = 180^{\circ}
$$

This simplifies to:

$$
100^{\circ} + 2B = 180^{\circ}
$$

Now, we can solve for $$ B $$:

$$
2B = 180^{\circ} - 100^{\circ}
$$
$$
2B = 80^{\circ}
$$
$$
B = \frac{80^{\circ}}{2} = 40^{\circ}
$$

Thus, the measures of the other two angles $$ B $$ and $$ C $$ are both $$ 40^{\circ} $$.

In conclusion, the possible measures for the other two angles in the isosceles triangle are:

- $$ 40^{\circ} $$ and $$ 40^{\circ} $$.
The other two angles are both $$ 40^{\circ} $$.

1) One angle of an isosceles triangle measures \( 100^{\circ} \). What measures are possible for the other two angles? Choose all that apply.