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Finding Right Triangle Angles When One Is Expressed Relative to Another

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Finding Right Triangle Angles Given One Angle is 50 Degrees More Than the Smallest

Apply the geometry problem-solving strategy to find the angle measures of a right triangle when one angle is defined in relation to the smallest angle.

Problem: The measure of one angle of a right triangle is $50$ degrees more than the measure of the smallest angle. Find the measures of all three angles.

Read the problem.
Identify what you are looking for: the measures of all three angles.
Name: Choose a variable to represent the smallest angle. Let $a$ be the measure of the smallest angle. The second angle is $50$ degrees more, so its measure is $a + 50$ . The third angle is a right angle, measuring $90^{\circ}$ .
Translate: Write the triangle angle sum property equation and substitute the known expressions: $a + (a + 50) + 90 = 180$
Solve the equation. Combine like terms: $2a + 140 = 180$ . Subtract $140$ from both sides: $2a = 40$ . Divide by $2$ : $a = 20$ . Substitute $a$ to find the other angles: the second angle is $a + 50 = 20 + 50 = 70$ , and the third angle is $90^{\circ}$ .
Check the solutions: Does $20 + 70 + 90 = 180$ ? Yes, $180 = 180$ $\checkmark$ .
Answer: The three angles measure $20^{\circ}$ , $70^{\circ}$ , and $90^{\circ}$ .

Updated 2026-05-02

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OpenStax Intermediate Algebra

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