Question: x°
135°
2x°
Graph: a single triangle-like broken line on a horizontal base, with angle x° near the left base, 135° at the top vertex, and 2x° near the right base; position_hint: center
Select the best classification for the triangle by its angles.
Equiangular
Obtuse
Right
Acute
1. **State the problem:** We have a triangle with angles $x^\circ$, $135^\circ$, and $2x^\circ$. We need to classify the triangle by its angles.
2. **Use the triangle angle sum property:** The sum of the interior angles of any triangle is $180^\circ$.
3. **Set up the equation:**
$$x + 135 + 2x = 180$$
4. **Combine like terms:**
$$3x + 135 = 180$$
5. **Isolate $x$:**
$$3x = 180 - 135$$
$$3x = 45$$
6. **Divide both sides by 3:**
$$x = \frac{45}{3}$$
$$x = 15$$
7. **Find all angles:**
- Left angle: $x = 15^\circ$
- Top angle: $135^\circ$
- Right angle: $2x = 2 \times 15 = 30^\circ$
8. **Classify the triangle:**
- Since one angle is $135^\circ$ which is greater than $90^\circ$, the triangle is **obtuse**.
**Final answer:** The triangle is an **Obtuse** triangle.