Right Triangle Angles: Finding Two Missing Interior Angles

Question

Does every right triangle have an angle _____ The other two angles are _______

Video Solution

Solution Steps

00:00 Fill in the missing values
00:05 Draw a right triangle
00:12 Mark the remaining angles with letters A,B
00:19 The sum of angles in a triangle equals 180
00:29 Isolate the sum of the remaining angles
00:35 From the equation we can conclude that every second angle is less than 90 (acute)
00:48 Therefore in a right triangle there is one right angle and the rest are acute
00:51 This is the solution

Step-by-Step Solution

Let's analyze the problem to understand how the angles are defined in a right triangle.

A right triangle is defined as a triangle that has one angle equal to 9090^\circ. This is known as a right angle. Because the sum of all angles in any triangle must be 180180^\circ, the two remaining angles must add up to 9090^\circ (i.e., 18090180^\circ - 90^\circ).

In a right triangle, the right angle is always present, leaving the other two angles to be less than 9090^\circ each. These angles are called acute angles. An acute angle is an angle that is less than 9090^\circ.

To summarize, the angle types in a right triangle are:

  • One angle that is 9090^\circ (a right angle).
  • Two angles that are each less than 9090^\circ (acute angles).

Given the choices, the description "Straight, sharp" correlates to the angle types in a right triangle, as "Straight" can be associated with the 9090^\circ angle (though it's generally called a right angle) and "Sharp" correlates with acute angles.

Therefore, the correct aspect of the other two angles in a right triangle are straight (right) and sharp (acute), which matches the correct choice.

Therefore, the solution to the problem is Straight, sharp.

Answer

Straight, sharp