question 9 of 10

in the diagram below, $\overline{xy}$ and $\overline{yz}$ are tangent to $\odot o$. which expression gives the measure of $\angle xyz$?

a. $\frac{1}{2}(245^\circ - 115^\circ)$
b. $245^\circ + 115^\circ$
c. $245^\circ - 115^\circ$
d. $\frac{1}{2}(245^\circ + 115^\circ)$

Question

question 9 of 10

in the diagram below, $\overline{xy}$ and $\overline{yz}$ are tangent to $\odot o$. which expression gives the measure of $\angle xyz$?

a. $\frac{1}{2}(245^\circ - 115^\circ)$
b. $245^\circ + 115^\circ$
c. $245^\circ - 115^\circ$
d. $\frac{1}{2}(245^\circ + 115^\circ)$

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": [ "Angles Outside Circle Theorem" ], "new_concepts": [], "current_concepts": [ "Angles Outside Circle Theorem", "Tangent Line", "Arc Measure" ] } ## Identify the given geometric elements Using the **Angles Outside Circle Theorem** knowledge point $$ \begin{aligned} &\text{Tangents: } \overline{XY} \text{ and } \overline{YZ}\ &\text{Intercepted major arc: } \widehat{XWZ} = 245^\circ\ &\text{Intercepted minor arc: } \widehat{XZ} = 115^\circ \end{aligned} $$ ## Apply the theorem to find the angle expression Using the **Angles Outside Circle Theorem** knowledge point $$ \begin{aligned} &m\angle XYZ = \frac{1}{2}(m\widehat{XWZ} - m\widehat{XZ})\ &m\angle XYZ = \frac{1}{2}(245^\circ - 115^\circ) \end{aligned} $$

A. $\frac{1}{2}(245^\circ - 115^\circ)$

B. $245^\circ + 115^\circ$

C. $245^\circ - 115^\circ$

D. $\frac{1}{2}(245^\circ + 115^\circ)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Angles Outside Circle Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given geometric elements

Apply the theorem to find the angle expression

Answer: