find the measure of angle b.
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Question

Accepted Answer

{ "quality": "clear", "question_count": 8, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Vertical Angles Theorem", "Linear Pair Postulate", "Supplementary Angles" ], "new_concepts": [ "Adjacent Angles on a Line", "Angles Around a Point" ], "current_concepts": [ "Vertical Angles Theorem", "Linear Pair Postulate", "Supplementary Angles", "Adjacent Angles on a Line", "Angles Around a Point" ] } ## Analyze Question 17 Using the *Linear Pair Postulate* and *Supplementary Angles* knowledge points $$ \begin{aligned} &50^\circ + b = 180^\circ \ &b = 180^\circ - 50^\circ = 130^\circ \end{aligned} $$ ## Analyze Question 18 Using the *Vertical Angles Theorem* knowledge point $$ b = 55^\circ $$ ## Analyze Question 19 Using the *Linear Pair Postulate* and *Supplementary Angles* knowledge points $$ \begin{aligned} &97^\circ + b = 180^\circ \ &b = 180^\circ - 97^\circ = 83^\circ \end{aligned} $$ ## Analyze Question 20 Using the *Vertical Angles Theorem* knowledge point $$ b = 58^\circ $$ ## Analyze Question 21 Using the *Linear Pair Postulate* and *Supplementary Angles* knowledge points $$ \begin{aligned} &89^\circ + b = 180^\circ \ &b = 180^\circ - 89^\circ = 91^\circ \end{aligned} $$ ## Analyze Question 22 The angle marked with a square is a right angle ($90^\circ$). The three angles lie on a straight line. Using the *Supplementary Angles* knowledge point $$ \begin{aligned} &63^\circ + 90^\circ + b = 180^\circ \ &153^\circ + b = 180^\circ \ &b = 180^\circ - 153^\circ = 27^\circ \end{aligned} $$ ## Analyze Question 23 The two adjacent angles form a right angle, indicated by the square corner symbol. Using the *Complementary Angles* knowledge point $$ \begin{aligned} &55^\circ + b = 90^\circ \ &b = 90^\circ - 55^\circ = 35^\circ \end{aligned} $$ ## Analyze Question 24 Using the *Linear Pair Postulate* and *Supplementary Angles* knowledge points $$ \begin{aligned} &114^\circ + b = 180^\circ \ &b = 180^\circ - 114^\circ = 66^\circ \end{aligned} $$ | No. | Answer | |---|---| | 17 | $b = 130^\circ$ | | 18 | $b = 55^\circ$ | | 19 | $b = 83^\circ$ | | 20 | $b = 58^\circ$ | | 21 | $b = 91^\circ$ | | 22 | $b = 27^\circ$ | | 23 | $b = 35^\circ$ | | 24 | $b = 66^\circ$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Angle Relationships" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze Question 17

Analyze Question 18

Analyze Question 19

Analyze Question 20

Analyze Question 21

Analyze Question 22

Analyze Question 23

Analyze Question 24

Answer:

No.	Answer
18	\(b = 55^\circ\)
19	\(b = 83^\circ\)
20	\(b = 58^\circ\)
21	\(b = 91^\circ\)
22	\(b = 27^\circ\)
23	\(b = 35^\circ\)
24	\(b = 66^\circ\)