question 21 of 25

in the diagram below, $m\widehat{pr} = 140^{\circ}$ and $m\widehat{qs} = 106^{\circ}$. what is the measure of $\angle ptr$?

a. $106^{\circ}$
b. $246^{\circ}$
c. $123^{\circ}$
d. $140^{\circ}$

Question

question 21 of 25

in the diagram below, $m\widehat{pr} = 140^{\circ}$ and $m\widehat{qs} = 106^{\circ}$. what is the measure of $\angle ptr$?

a. $106^{\circ}$
b. $246^{\circ}$
c. $123^{\circ}$
d. $140^{\circ}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circle Theorems" ], "new_concepts": [ "Angles of Intersecting Chords Theorem" ], "current_concepts": [ "Circle Theorems", "Angles of Intersecting Chords Theorem" ] } ## Identify the given arc measures and target angle $$ \begin{aligned} &m\widehat{PR} = 140^\circ\ &m\widehat{QS} = 106^\circ\ &\text{Target: } m\angle PTR \end{aligned} $$ ## Apply the Angles of Intersecting Chords Theorem $$ \begin{aligned} m\angle PTR &= \frac{m\widehat{PR} + m\widehat{QS}}{2}\ m\angle PTR &= \frac{140^\circ + 106^\circ}{2} \end{aligned} $$ ## Calculate the final angle measure $$ \begin{aligned} m\angle PTR &= \frac{246^\circ}{2}\ m\angle PTR &= 123^\circ \end{aligned} $$

A. $106^\circ$

B. $246^\circ$

C. $123^\circ$

D. $140^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Theorems" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given arc measures and target angle

Apply the Angles of Intersecting Chords Theorem

Calculate the final angle measure

Answer: