Question

in isosceles △tuv, • ∠u and ∠v are the base angles, and • m∠u is 56.5°. what is m∠t? a. 56.5° b. 67° c. 123.5° d. 113°

Explanation:

Step1: Recall base - angle property

In an isosceles triangle, base angles are equal. So $m\angle U=m\angle V = 56.5^{\circ}$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle T=x$. Then $x + m\angle U+m\angle V=180^{\circ}$. Substitute $m\angle U = 56.5^{\circ}$ and $m\angle V = 56.5^{\circ}$ into the equation: $x+56.5^{\circ}+56.5^{\circ}=180^{\circ}$.

Step3: Solve for $m\angle T$

$x=180^{\circ}-(56.5^{\circ}+56.5^{\circ})=180^{\circ}-113^{\circ}=67^{\circ}$.

Answer:

B. $67^{\circ}$