Question

1. in a right triangle, the measure of one acute angle is 2 times the sum of the measure of the other acute angle and 6. find the measure of each acute angle.

a. 20°, 70°
b. 26°, 64°
c. 34°, 56°
d. 23°, 57°

Explanation:

Step1: Set up equations

Let one acute angle be \(x\) and the other be \(y\). In a right - triangle, \(x + y=90^{\circ}\) (because the sum of angles in a triangle is \(180^{\circ}\) and one angle is \(90^{\circ}\)). Also, given \(x = 2(y + 6)\).

Step2: Substitute and solve

Substitute \(x = 2(y + 6)\) into \(x + y=90\).

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Step3: Find the other angle

Substitute \(y = 26\) into \(x + y=90\), then \(x=90 - 26=64\)

Answer:

b. \(26^{\circ},64^{\circ}\)