Question

congruent triangles quiz
what kind of triangle is △bcd?
o acute
o equiangular
o right
o obtuse

Explanation:

Step1: Find an interior - angle at D

The exterior angle at D is 130°. Using the exterior - angle property (an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles), the interior angle at D, $\angle BDC=180^{\circ}- 130^{\circ}=50^{\circ}$.

Step2: Find the third angle

We know one angle $\angle BCD = 70^{\circ}$ and $\angle BDC = 50^{\circ}$. Using the angle - sum property of a triangle ($\angle DBC+\angle BCD+\angle BDC = 180^{\circ}$), we find $\angle DBC=180^{\circ}-(70^{\circ}+50^{\circ}) = 60^{\circ}$.

Step3: Classify the triangle

Since all angles $\angle DBC = 60^{\circ}$, $\angle BCD = 70^{\circ}$, and $\angle BDC = 50^{\circ}$ are less than 90°, the triangle is acute.

Answer:

acute