Question

8.g.a.5 6 toru rode his bike from his house to the library, to the park and then back home. toru realized that his route made an isosceles triangle and that the library was the exact same distance from both his house and the park. what is the measure of the angle at the library? library park house 70° 70° 110° 180° 40°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$.

Step2: Identify base - angles of isosceles triangle

In an isosceles triangle, if the library is equidistant from the house and the park, the angles at the house and the park are equal. Given the angle at the house is $70^{\circ}$, so the angle at the park is also $70^{\circ}$.

Step3: Calculate the angle at the library

Let the angle at the library be $x$. Using the angle - sum property of a triangle ($x + 70^{\circ}+70^{\circ}=180^{\circ}$), we can solve for $x$.
$x=180^{\circ}-(70^{\circ} + 70^{\circ})=40^{\circ}$

Answer:

D. $40^{\circ}$