what is $m\angle b$?

what is $m\widehat{bc}$?

$\triangle abc$ is a and triangle.

Question

what is $m\angle b$?

what is $m\widehat{bc}$?

$\triangle abc$ is a   and   triangle.

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inscribed Angle Theorem" ], "new_concepts": [ "Inscribed Right Triangle Theorem" ], "current_concepts": [ "Inscribed Angle Theorem", "Inscribed Right Triangle Theorem", "Triangle Angle Sum Theorem" ] } ## Identify the angle inscribed in the semicircle $$ \begin{aligned} &\text{Segment } AB \text{ passes through the center } O, \text{ so } AB \text{ is a diameter.}\ &m\angle C = 90^\circ \end{aligned} $$ ## Calculate the measure of angle B $$ \begin{aligned} &m\angle B = 180^\circ - (m\angle C + m\angle A)\ &m\angle B = 180^\circ - (90^\circ + 71^\circ) = 19^\circ \end{aligned} $$ ## Calculate the measure of arc BC $$ \begin{aligned} &m\overparen{BC} = 2 \times m\angle A\ &m\overparen{BC} = 2 \times 71^\circ = 142^\circ \end{aligned} $$ ## Classify triangle ABC $$ \begin{aligned} &\text{Since } m\angle C = 90^\circ, \Delta ABC \text{ is a right triangle.}\ &\text{Since all angles } (71^\circ, 19^\circ, 90^\circ) \text{ are distinct, it is a scalene triangle.} \end{aligned} $$ ## Question 1 What is $m\angle B$? 19$^\circ$ ## Question 2 What is $m\overparen{BC}$? 142$^\circ$ ## Question 3 $\Delta ABC$ is a right and scalene triangle. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Inscribed Angle Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the angle inscribed in the semicircle

Calculate the measure of angle B

Calculate the measure of arc BC

Classify triangle ABC

Answer:

Question 1

Question 2

Question 3