Question

calculate the size of ∠c, the third angle in each triangle, and classify the triangle as acute, obtuse, or right in problems 1 to 6.

1. ∠a = 35° and ∠b = 55°
2. ∠a = 25° and ∠b = 40°
3. ∠a = 101° and ∠b = 36°
4. ∠a = 78° and ∠b = 43°
5. ∠a = 90° and ∠b = 29°
6. ∠a = 32° and ∠b = 51°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $\angle C=180^{\circ}-\angle A - \angle B$.

Step2: Determine triangle type

If $\angle C<90^{\circ}$, $\angle A<90^{\circ}$ and $\angle B<90^{\circ}$, the triangle is acute. If one angle is $90^{\circ}$, it is a right - triangle. If one angle is greater than $90^{\circ}$, it is an obtuse - triangle.

Problem 1

Step1: Calculate $\angle C$

$\angle C = 180^{\circ}-35^{\circ}-55^{\circ}=90^{\circ}$

Step2: Classify the triangle

Since $\angle C = 90^{\circ}$, the triangle is a right - triangle.

Answer:

$\angle C = 90^{\circ}$, right - triangle

Problem 2

Step1: Calculate $\angle C$

$\angle C=180^{\circ}-25^{\circ}-40^{\circ}=115^{\circ}$

Step2: Classify the triangle

Since $\angle C>90^{\circ}$, the triangle is an obtuse - triangle.