Question

In triangle STU, u2 = s2 + t2. Triangle STU has sides s, t, u opposite to the corresponding vertices S, T, U Which equation is true about the measure of the angles of the triangle? The measure of angle STU is equal to 100 degrees The measure of angle SUT is equal to 90 degrees The measure of angle STU plus the measure of angle TSU is equal to 80 degrees The measure of angle STU plus the measure of angle TSU is equal to 70 degrees

Answer 1

Answer:

90 degrees

Step-by-step explanation:

Answer 2

Answer:
The measure of angle SUT is equal to 90 degrees

Explanation:
The Pythagorean theorem states that:
"In any right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides"
In other words:
(hypotenuse)² = (first side)² + (second side)²

Now, for the given, we have:
u² = s² + t²
This means that the given triangle UST is a right-angled triangle and that side "u" is its hypotenuse.

According to the given, the angle opposite to side "u" is angle U. This means that angle U is the right-angle in this triangle.

Based on the above:
angle U = 90°
angle S + angle T = 180 - 90 = 90°

Now, comparing our deductions to the given choices, we can conclude that the correct choice is:
The measure of angle SUT is equal to 90 degrees

Hope this helps :)