if $\angle rst$ and $\angle xyz$ are vertical angles, and $m\angle rst$ is equal to $25^\circ$, then what is $m\angle xyz$?

$m\angle xyz = \quad^\circ$

Question

if $\angle rst$ and $\angle xyz$ are vertical angles, and $m\angle rst$ is equal to $25^\circ$, then what is $m\angle xyz$?

$m\angle xyz = \quad^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Vertical Angles" ], "current_concepts": [ "Vertical Angles", "Angle Measure" ] } ## Identify the given information We are given that $\angle RST$ and $\angle XYZ$ are vertical angles. We are also given that $m\angle RST = 25^\circ$. ## Apply the vertical angles theorem Vertical angles are opposite angles formed by intersecting lines. The **Vertical Angles Theorem** states that vertical angles are always congruent. This means their measures are equal: $$m\angle XYZ = m\angle RST$$ ## Solve for the unknown measure Substitute the given value of $m\angle RST$ into the equation: $$m\angle XYZ = 25^\circ$$ If $\angle RST$ and $\angle XYZ$ are vertical angles, and $m\angle RST$ is equal to $25^\circ$, then what is $m\angle XYZ$? $m\angle XYZ =$ 25$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Vertical Angles" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given information

Apply the vertical angles theorem

Solve for the unknown measure

Answer: