Question

An isosceles triangle contains three angles that measure ${40}^{\circ },x^{\circ }$, and $y^{\circ }$. Which of the following CANNOT be true?

• A. $x=y$
• B. $x=50$
• C. $x-y=60$
• D. $x=70$
• E. $x=100$

Answer 1

Answer: (B)

$x=50$

Every triangle has three angles that add up to $180°$, and an isosceles triangle has two equivalent angles.

Therefore, the three angles of this triangle are either $40°+40°+100°$ or $40°+70°+70°$. In any case, this triangle can’t include a $50°$ angle.

Hence, $x=50$.