if $m\angle x = 34^{\circ}$ and $m\angle z = 26^{\circ}$, what is $m\angle y$?

$m\angle y = 26^{\circ}$
$m\angle y = 34^{\circ}$
$m\angle y = 60^{\circ}$
$m\angle y = 120^{\circ}$

Question

if $m\angle x = 34^{\circ}$ and $m\angle z = 26^{\circ}$, what is $m\angle y$?

$m\angle y = 26^{\circ}$
$m\angle y = 34^{\circ}$
$m\angle y = 60^{\circ}$
$m\angle y = 120^{\circ}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Triangle Angle Sum Theorem" ], "current_concepts": [ "Triangle Angle Sum Theorem" ] } ## Identify the given values We are given a triangle $XYZ$ with: - $m\angle X = 34^\circ$ - $m\angle Z = 26^\circ$ ## State the relevant theorem The sum of interior angles in any triangle is always $180^\circ$. $$ m\angle X + m\angle Y + m\angle Z = 180^\circ $$ ## Substitute and solve for the unknown angle Substitute the given values into the equation: $$ 34^\circ + m\angle Y + 26^\circ = 180^\circ $$ $$ 60^\circ + m\angle Y = 180^\circ $$ $$ m\angle Y = 120^\circ $$

$m\angle Y = 26^\circ$

$m\angle Y = 34^\circ$

$m\angle Y = 60^\circ$

$m\angle Y = 120^\circ$

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QUESTION IMAGE

Question

Explanation:

Identify the given values

State the relevant theorem

Substitute and solve for the unknown angle

Answer: