If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

Options

A. an isosceles triangle
B. an obtuse triangle
C. an equilateral triangle
D. a right triangle

Answer

To solve the question, "If one angle of a triangle is equal to the sum of the other two angles, then the triangle is...", we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Triangle Angle Sum Property**:
- In any triangle, the sum of the three interior angles is always equal to 180 degrees. This can be expressed as:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]

2. **Setting Up the Given Condition**:
- According to the problem, we are given that one angle (let's say Angle A) is equal to the sum of the other two angles (Angle B and Angle C). This can be written as:
\[ \text{Angle A} = \text{Angle B} + \text{Angle C} \]

3. **Substituting into the Angle Sum Property**:
- We can substitute the expression for Angle A into the angle sum property equation:
\[ (\text{Angle B} + \text{Angle C}) + \text{Angle B} + \text{Angle C} = 180^\circ \]
- This simplifies to:
\[ 2(\text{Angle B} + \text{Angle C}) = 180^\circ \]

4. **Dividing Both Sides by 2**:
- To find the sum of Angle B and Angle C, we divide both sides by 2:
\[ \text{Angle B} + \text{Angle C} = 90^\circ \]

5. **Conclusion about Angle A**:
- Since we established that Angle A is equal to the sum of Angle B and Angle C, we can now conclude:
\[ \text{Angle A} = 90^\circ \]
- Therefore, if one angle of a triangle is equal to the sum of the other two angles, that angle must be 90 degrees.

6. **Final Conclusion**:
- A triangle with one angle measuring 90 degrees is classified as a right-angled triangle. Hence, we conclude:
\[ \text{The triangle is a right angle triangle.} \]