To find the missing angle in the triangle shown, let's analyze the information given:
Step 1: Understand the Triangle
We are given a triangle $ \triangle ABC $ with:
- A right angle at vertex $ B $ (indicated by the square symbol).
- Angle at vertex $ A $ is $ 40^\circ $.
- We need to find the measure of angle at vertex $ C $, marked with a question mark.
Step 2: Use the Triangle Angle Sum Theorem
The
sum of the interior angles in any triangle is always:
$$
180^\circ
$$
So:
$$
\angle A + \angle B + \angle C = 180^\circ
$$
We know:
- $ \angle A = 40^\circ $
- $ \angle B = 90^\circ $ (since it's a right angle)
Substitute into the equation:
$$
40^\circ + 90^\circ + \angle C = 180^\circ
$$
$$
130^\circ + \angle C = 180^\circ
$$
$$
\angle C = 180^\circ - 130^\circ = 50^\circ
$$
✔ Final Answer:
$$
\boxed{50^\circ}
$$
Explanation:
In a right triangle, the two non-right angles are complementary (they add up to $ 90^\circ $). Since one acute angle is $ 40^\circ $, the other must be:
$$
90^\circ - 40^\circ = 50^\circ
$$
So, the missing angle at $ C $ is $ \boxed{50^\circ} $.
Parent Tip: Review the logic above to help your child master the concept of triangle missing.
