find the values of $x$ and $y$ in the following diagram:

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Angle Sum Theorem", "Supplementary Angles" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Supplementary Angles", "Linear Pair" ] } ## Find the value of y Using the *Triangle Angle Sum Theorem* knowledge point $$ \begin{aligned} 90^\circ + 50^\circ + (8y)^\circ &= 180^\circ \ 140 + 8y &= 180 \ 8y &= 40 \ y &= 5 \end{aligned} $$ ## Find the value of x Using the *Supplementary Angles* knowledge point $$ \begin{aligned} (8y)^\circ + (5x + 55)^\circ &= 180^\circ \ 8(5) + 5x + 55 &= 180 \ 40 + 5x + 55 &= 180 \ 5x + 95 &= 180 \ 5x &= 85 \ x &= 17 \end{aligned} $$ $x = 17$, $y = 5$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Angle Sum Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Find the value of y

Find the value of x

Answer: