determine an expression for $x$ in terms of $a$ based on the following diagram:

$x = -2a + 115$
$x = 2a + 155$
$x = -2a - 155$
$x = 2a - 115$

Question

determine an expression for $x$ in terms of $a$ based on the following diagram:

$x = -2a + 115$
$x = 2a + 155$
$x = -2a - 155$
$x = 2a - 115$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Angle Sum Theorem", "Supplementary Angles" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Supplementary Angles" ] } ## Find the interior angles of the triangle $$ \begin{aligned} &\theta_1 = 180^\circ - 135^\circ = 45^\circ\ &\theta_2 = 2a + 20^\circ\ &\theta_3 = x \end{aligned} $$ ## Apply the Triangle Angle Sum Theorem $$ \begin{aligned} &45 + (2a + 20) + x = 180\ &x + 2a + 65 = 180 \end{aligned} $$ ## Solve for x in terms of a $$ \begin{aligned} &x = 180 - 65 - 2a\ &x = -2a + 115 \end{aligned} $$

(A) $x = -2a + 115$

(B) $x = 2a + 155$

(C) $x = -2a - 155$

(D) $x = 2a - 115$

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

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QUESTION IMAGE

Question

Explanation:

Find the interior angles of the triangle

Apply the Triangle Angle Sum Theorem

Solve for x in terms of a

Answer: