Question

e measure of angle a?

(10^{\circ})

(15^{\circ})

(90^{\circ})

(105^{\circ})

Explanation:

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<reasoning>

Identify the given angles in right triangle ABC

\[

$$\begin{aligned} &m\angle B = 90^\circ \\ &m\angle C = 75^\circ \end{aligned}$$

\]

Apply the Triangle Angle Sum Theorem

\[

$$\begin{aligned} &m\angle A + m\angle B + m\angle C = 180^\circ \\ &m\angle A + 90^\circ + 75^\circ = 180^\circ \end{aligned}$$

\]

Solve for the measure of angle A

\[

$$\begin{aligned} &m\angle A + 165^\circ = 180^\circ \\ &m\angle A = 180^\circ - 165^\circ \\ &m\angle A = 15^\circ \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(10^\circ\)</mcq-option>
<mcq-correct>(B) \(15^\circ\)</mcq-correct>
<mcq-option>(C) \(90^\circ\)</mcq-option>
<mcq-option>(D) \(105^\circ\)</mcq-option>
</answer>

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"question_type": "Multiple Choice",
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</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Identify the given angles in right triangle ABC

\[

$$\begin{aligned} &m\angle B = 90^\circ \\ &m\angle C = 75^\circ \end{aligned}$$

\]

Apply the Triangle Angle Sum Theorem

\[

$$\begin{aligned} &m\angle A + m\angle B + m\angle C = 180^\circ \\ &m\angle A + 90^\circ + 75^\circ = 180^\circ \end{aligned}$$

\]

Solve for the measure of angle A

\[

$$\begin{aligned} &m\angle A + 165^\circ = 180^\circ \\ &m\angle A = 180^\circ - 165^\circ \\ &m\angle A = 15^\circ \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(10^\circ\)</mcq-option>
<mcq-correct>(B) \(15^\circ\)</mcq-correct>
<mcq-option>(C) \(90^\circ\)</mcq-option>
<mcq-option>(D) \(105^\circ\)</mcq-option>
</answer>

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