2. in the figure, $\angle bac$ measures $35^\circ$, $\angle abc$ measures $95^\circ$, and points $b$, $c$, and $d$ are collinear. what is the measure of $\angle acd$?

f. $125^\circ$
g. $130^\circ$
h. $140^\circ$
j. $145^\circ$

Question

2. in the figure, $\angle bac$ measures $35^\circ$, $\angle abc$ measures $95^\circ$, and points $b$, $c$, and $d$ are collinear. what is the measure of $\angle acd$?

f. $125^\circ$
g. $130^\circ$
h. $140^\circ$
j. $145^\circ$

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": [ "Triangle Angle Sum Theorem" ], "new_concepts": [ "Exterior Angle Theorem" ], "current_concepts": [ "Triangle Angle Sum Theorem", "Exterior Angle Theorem", "Linear Pair" ] } ## Identify the given values and target angle The given values in $\triangle ABC$ are: - $m\angle BAC = 35^\circ$ - $m\angle ABC = 95^\circ$ - Points $B$, $C$, and $D$ are collinear, making $\angle ACD$ an exterior angle to $\triangle ABC$. The target is to find the measure of $\angle ACD$. ## Calculate the exterior angle measure Using the **Triangle Angle Sum Theorem** knowledge point $$ \begin{aligned} m\angle ACD &= m\angle BAC + m\angle ABC \ m\angle ACD &= 35^\circ + 95^\circ \ m\angle ACD &= 130^\circ \end{aligned} $$

F. $125^\circ$

G. $130^\circ$

H. $140^\circ$

J. $145^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Exterior Angle Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and target angle

Calculate the exterior angle measure

Answer: