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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 30 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 $30$ 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: Let $a$ be the measure of the smallest angle. The second angle is $30$ degrees more, giving $a + 30$ . The third angle is a right angle, measuring $90^{\circ}$ .
Translate: Write the sum of angles formula for a triangle and substitute: $a + (a + 30) + 90 = 180$
Solve the equation. Combine all constants and like terms: $2a + 120 = 180$ . Subtract $120$ from both sides: $2a = 60$ . Divide by $2$ : $a = 30$ . The second angle is $a + 30 = 30 + 30 = 60$ , and the third angle is $90^{\circ}$ .
Check the solutions: Does $30 + 60 + 90 = 180$ ? Yes, $180 = 180$ $\checkmark$ .
Answer: The three angles measure $30^{\circ}$ , $60^{\circ}$ , and $90^{\circ}$ .

Updated 2026-05-02

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OpenStax Intermediate Algebra

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