which statement is true about $\angle cpb$?

it is supplementary to $\angle apc$.
it is complementary to $\angle apc$.
it is congruent to $\angle apc$.
it is linear to $\angle apd$.

Question

which statement is true about $\angle cpb$?

it is supplementary to $\angle apc$.
it is complementary to $\angle apc$.
it is congruent to $\angle apc$.
it is linear to $\angle apd$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Linear Pair", "Supplementary Angles" ], "new_concepts": [], "current_concepts": [ "Linear Pair", "Supplementary Angles", "Vertical Angles" ] } ## Identify the geometric relationship between the angles Using the *Linear Pair* and *Supplementary Angles* knowledge points $$ \begin{aligned} &\text{Line } AB \text{ is a straight line intersecting line } CD \text{ at point } P.\ &\angle CPB \text{ and } \angle APC \text{ lie on the straight line } AB.\ &\angle CPB + \angle APC = 180^\circ \end{aligned} $$ ## Evaluate the given statements Using the *Supplementary Angles* knowledge point $$ \begin{aligned} &\angle CPB + \angle APC = 180^\circ \implies \angle CPB \text{ is supplementary to } \angle APC. \end{aligned} $$

It is supplementary to $\angle APC$.

It is complementary to $\angle APC$.

It is congruent to $\angle APC$.

It is linear to $\angle APD$.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Linear Pair" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the geometric relationship between the angles

Evaluate the given statements

Answer: