bisects $\angle dbc$. find the value of $x$ and $m\angle abc$.

press the hotspot and type your answer. do not include symbols, just provide your numerical answer.

$x = $ ______
$m\angle abc = $ ______

Question

bisects $\angle dbc$. find the value of $x$ and $m\angle abc$.

press the hotspot and type your answer. do not include symbols, just provide your numerical answer.

$x = $ ______
$m\angle abc = $ ______

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Angle Bisector Definition", "Algebraic Angle Solving" ], "new_concepts": [], "current_concepts": [ "Angle Bisector Definition", "Algebraic Angle Solving", "Angle Measurement" ] } ## Set up the geometric equation Using the *Angle Bisector Definition* and *Algebraic Angle Solving* knowledge points $$ \begin{aligned} &m\angle DBA = m\angle ABC\ &x + 40 = 5x \end{aligned} $$ ## Solve for x Using the *Algebraic Angle Solving* knowledge point $$ \begin{aligned} &40 = 4x\ &x = 10 \end{aligned} $$ ## Calculate the measure of angle ABC Using the *Angle Measurement* and *Algebraic Angle Solving* knowledge points $$ \begin{aligned} &m\angle ABC = 5x\ &m\angle ABC = 5(10) = 50 \end{aligned} $$ If $\vec{BA}$ bisects $\angle DBC$, find the value of $x$ and $m\angle ABC$. $x =$ 10 $m\angle ABC =$ 50 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Angle Bisector Definition" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the geometric equation

Solve for x

Calculate the measure of angle ABC

Answer: