find $x$ so that $kh \parallel gm$.

image showing a trapezoid-like figure with vertices $d, e, h, m, g, k$. a perpendicular line segment $dm$ is drawn from $d$ to the base $gm$, intersecting $kh$ at a right angle. the angle $\angle dmg$ is indicated with a right-angle symbol, and the adjacent angle is labeled $(8x + 26)^\circ$.

a $x = 90$
b $x = 64$
c $x = 8$
d $x = 16$

Question

find $x$ so that $kh \parallel gm$.

image showing a trapezoid-like figure with vertices $d, e, h, m, g, k$. a perpendicular line segment $dm$ is drawn from $d$ to the base $gm$, intersecting $kh$ at a right angle. the angle $\angle dmg$ is indicated with a right-angle symbol, and the adjacent angle is labeled $(8x + 26)^\circ$.

a $x = 90$
b $x = 64$
c $x = 8$
d $x = 16$

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": [ "Consecutive Interior Angles Theorem", "Parallel Lines Cut by a Transversal", "Linear Equations" ], "new_concepts": [], "current_concepts": [ "Consecutive Interior Angles Theorem", "Parallel Lines Cut by a Transversal", "Linear Equations" ] } ## Identify the geometric relationship Using the **Parallel Lines Cut by a Transversal** and **Consecutive Interior Angles Theorem** knowledge points $$ \begin{aligned} &KH \parallel GM \ &DM \perp KH \implies \angle DMK + \angle MKH = 180^\circ \ &\angle DMK = 90^\circ \implies \angle DMG = 90^\circ \end{aligned} $$ ## Set up the algebraic equation Using the **Linear Equations** knowledge point $$ \begin{aligned} &8x + 26 = 90 \end{aligned} $$ ## Solve for x Using the **Linear Equations** knowledge point $$ \begin{aligned} &8x = 90 - 26 \ &8x = 64 \ &x = 8 \end{aligned} $$

A $x = 90$

B $x = 64$

C $x = 8$

D $x = 16$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Lines Cut by a Transversal" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric relationship

Set up the algebraic equation

Solve for x

Answer: