in the following figure, $\overline{eb}$ and $\overline{dc}$ intersect at point a.
what is the value of $x$ in the figure?
$x = $

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Angle Sum Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Vertical Angles", "Isosceles Triangle Theorem" ] } ## Find the vertical angle in the upper triangle $$ \angle EAD = 118^\circ \implies \angle EAC = 180^\circ - 118^\circ = 62^\circ $$ $$ \angle EAD = \angle CAB = 118^\circ \implies \angle EAc = 180^\circ - 118^\circ = 62^\circ $$ $$ \angle EAc = \angle DAB = 62^\circ $$ ## Determine the angles of the lower triangle $$ \begin{aligned} &AC = 3.6,\quad AB = 3.8 \quad (\text{not equal})\ &AE = 3.6,\quad AD = 3.8\ &\angle CAB = 118^\circ,\quad \angle B = 30^\circ\ &\angle C = 180^\circ - (118^\circ + 30^\circ) = 32^\circ \end{aligned} $$ ## Solve for x using triangle congruence $$ \begin{aligned} &AE = AC = 3.6\ &AD = AB = 3.8\ &\angle EAD = \angle CAB = 118^\circ\ &\triangle EAD \cong \triangle CAB \quad (\text{SAS})\ &x^\circ = \angle E = \angle C = 32^\circ \implies x = 32 \end{aligned} $$ What is the value of $x$ in the figure? $x =$ 32 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Congruence Criteria" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Find the vertical angle in the upper triangle

Determine the angles of the lower triangle

Solve for x using triangle congruence

Answer: