Right Angle
Worked Example
Problem: A triangle has angles measuring 90°, 35°, and an unknown angle. Confirm that the 90° angle is a right angle, then find the missing angle.
Step 1: Identify the right angle. The 90° angle is, by definition, a right angle. In diagrams, it is marked with a small square in the corner rather than a curved arc.
Step 2: Recall that the interior angles of any triangle sum to 180°.
90°+35°+x=180°
Step 3: Solve for the unknown angle.
x=180°−90°−35°=55°
Answer: The missing angle is 55°. Because one of the three angles is exactly 90°, this is a right triangle.
Another Example
Problem: Two lines intersect and one of the four angles formed measures 90°. What are the measures of the other three angles?
Step 1: When two lines intersect, vertically opposite angles are equal. The angle opposite the 90° angle is also 90°.
Step 2: Adjacent angles on a straight line are supplementary (they add to 180°). Each angle adjacent to the 90° angle measures:
180°−90°=90°
Step 3: Therefore all four angles are 90°. When one angle at an intersection is a right angle, the two lines are perpendicular, and every angle at that intersection is a right angle.
Answer: All four angles measure 90°. The two lines are perpendicular.
Frequently Asked Questions
How many degrees is a right angle?
A right angle is exactly 90°. This is one-quarter of a full rotation (360°) and half of a straight angle (180°).
How do you identify a right angle in a diagram?
A right angle is shown with a small square symbol drawn in the corner where the two lines meet. This distinguishes it from other angles, which are typically marked with a curved arc.
Right Angle vs. Straight Angle
A right angle measures 90° and represents a quarter turn. A straight angle measures 180° and forms a straight line — exactly two right angles placed side by side. Both are specific, named angle measures, but they look very different: one is an "L" shape, the other is a flat line.
Why It Matters
Right angles are foundational in geometry and everyday construction. Buildings, screens, book pages, and floor tiles all rely on 90° corners to fit together properly. In mathematics, right angles define perpendicular lines, underpin the Pythagorean theorem, and are essential to trigonometry — the sine, cosine, and tangent ratios are originally defined using right triangles.
Common Mistakes
Mistake: Assuming an angle is 90° just because it looks like a square corner in a diagram.
Correction: Only treat an angle as a right angle if it is explicitly marked with the small square symbol or stated to be 90°. Diagrams are often not drawn to scale.
Mistake: Confusing a right angle with a "right" (correct) answer — or thinking "right" means the angle points to the right.
Correction: The word "right" here comes from the Latin "rectus," meaning upright or proper. It refers to the 90° measure, not a direction.
Related Terms
- Angle — General term; a right angle is a specific case
- Right Triangle — A triangle containing one right angle
- Perpendicular — Lines that meet at a right angle
- Degree — Unit used to measure angles, including 90°
- Acute Angle — An angle measuring less than 90°
- Obtuse Angle — An angle measuring more than 90° but less than 180°
- Straight Angle — An angle of 180°, equal to two right angles
- Complementary Angles — Two angles that sum to one right angle (90°)