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Angle \( qpt \) is a right angle. The measure of angle \( qps \) is 20° more than the measure of angle \( spt \). What is the measure of angle \( qps \)?

Answer :

Final answer:

The measure of angle qps in a right triangle, if it is 20° more than the measure of the other non-right angle (angle spt), is 55°.

Explanation:

The question is related to the properties of angles in a right triangle. According to the problem, angle qpt is a right angle, therefore, the sum of angle qps and angle spt is 90°, because in a right triangle the two non-right angles add up to 90°. If angle qps is 20° more than angle spt, we can set up the equation: angle qps = angle spt + 20°. Combining this with the fact that angle qps + angle spt = 90°, we can solve for angle qps:

  1. Substitute angle spt + 20° for angle qps in the second equation, we find that (angle spt + 20°) + angle spt = 90°.
  2. This simplifies to 2*angle spt + 20° = 90°.
  3. Subtracting 20° from both sides gives 2*angle spt = 70°.
  4. Dividing by 2, we find that angle spt = 35°.
  5. Substituting angle spt = 35° into the first equation gives us angle qps = 35° + 20° = 55°.

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