Question

in a right triangle, one unknown angle is 1.5 times as large as the other unknown angle. determine the measure of the missing angles.

\\(36^\circ\\) and \\(45^\circ\\)
\\(36^\circ\\) and \\(54^\circ\\)
\\(36^\circ\\) and \\(90^\circ\\)
\\(45^\circ\\) and \\(45^\circ\\)

Explanation:

Identify the properties of a right triangle

Using the Triangle Classification knowledge point

$$ \text{A right triangle contains one angle of } 90^\circ. $$

Set up the relationship between the acute angles

Using the Complementary Angles and Triangle Angle Sum Theorem knowledge points

$$
LATEXBLOCK0
$$

Solve the system of equations

Using the Complementary Angles knowledge point

$$
LATEXBLOCK1
$$

Calculate the second unknown angle

Using the Complementary Angles knowledge point

$$
LATEXBLOCK2
$$

Answer:

• (A) \(36^\circ\) and \(45^\circ\)
• (B) \(36^\circ\) and \(54^\circ\) (Correct answer)
• (C) \(36^\circ\) and \(90^\circ\)
• (D) \(45^\circ\) and \(45^\circ\)