Question

question 4 of 10
what are the measures of the angles in an isosceles right triangle?
a. 30°, 60°, and 90°
b. cannot be determined
c. 60°, 60°, and 90°
d. 45°, 45°, and 90°

Explanation:

Step1: Recall properties of isosceles right triangle

An isosceles right triangle has one right angle (90°) and two equal angles (since it's isosceles, two sides are equal, so their opposite angles are equal). Let the equal angles be \( x \).

Step2: Use triangle angle sum property

The sum of angles in a triangle is 180°. So, \( 90^\circ + x + x = 180^\circ \). Simplify: \( 90^\circ + 2x = 180^\circ \). Subtract 90°: \( 2x = 90^\circ \). Divide by 2: \( x = 45^\circ \). So angles are 45°, 45°, 90°.

Answer:

D. \( 45^\circ \), \( 45^\circ \), and \( 90^\circ \)