Question

preact 10 #2 math section a line is drawn through an isosceles right triangle, creating two triangles, a and b, as shown in the diagram below. if the area of a is equal to the area of b, what is the measure of angle x?

Explanation:

Step1: Recall properties of isosceles right - triangle

An isosceles right - triangle has angles 45°, 45°, 90°. When a line divides the triangle into two triangles of equal area, the line is a median (since a median of a triangle divides it into two triangles of equal area).

Step2: Analyze the angle formed

In an isosceles right - triangle, the median drawn from the right - angle vertex to the hypotenuse bisects the right - angle. So, if the right - angle is 90°, and the line (median) divides it, the measure of angle \(x\) is 45°.

Answer:

45°