Explain the connection between ∠2 and ∠B.
2 answers:
Answer:
∠2 ≅ ∠B
Step-by-step explanation:
Let the triangle be ABC,
Given that,
∠A = 50°
∠C = 65°
Using angle-sum property of the triangle,
∠A + ∠B + ∠C = 180°
50° + ∠B + 65° = 180°
∵ ∠B = 65° ...(i)
A.T.Q.
Two horizontal lines are extended making 3 angles. Two angles out of them are 50° and 65°.
Since the adjacent angles comprising a straight line is equals to 180°.
so,
∠2 + 50° + 65° = 180°
∠2 + 115° = 180°
∠2 = 180° - 115°
∵ ∠2 = 65° ...(ii)
Using (i) and (ii),
∠2 ≅ ∠B
Therefore, ∠2 and ∠B are congruent to one another .
Answer: Sample Response: The sum of the measures of the interior angles of a triangle is 180°. m∠B + 50 + 65 = 180, so m∠B = 65°. The sum of adjacent angles forming a straight line is also 180°. m∠2 + 50 + 65 =180, so m∠2 = 65°. The angles are congruent.
Step-by-step explanation: its the sample response
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