Triangle ABC is an isosceles right triangle. What is the measure of one of the base angles?

• A. $60°$
• B. $30°$
• C. $90°$
• D. $45°$

Answer: (D)

Verified step by step guidance

1. Recall that an isosceles right triangle has two sides of equal length and one right angle (90\(\degree\)).
2. Since the triangle is isosceles, the two base angles opposite the equal sides are congruent (have the same measure).
3. The sum of the interior angles in any triangle is always 180\(\degree\), so we can write the equation: 90\(\degree\) + 2x = 180\(\degree\), where x represents one of the base angles.
4. Solve for x by subtracting 90\(\degree\) from both sides: 2x = 180\(\degree\) - 90\(\degree\).
5. Divide both sides by 2 to find the measure of one base angle: x = \(\frac{180\degree - 90\degree}{2}\).