Question

Explain the connection between Ð2 and ÐB.

A triangle has angle measures 50 degrees, 65 degrees, and B. 2 lines extend from a horizontal line to form 3 angles. The angles are 50 degrees, 2, 65 degrees.

Answer 1

Answer:

∠2 is congruent to ∠B

Step-by-step explanation:

We should know that the sum of the interior angles of a triangle is 180°.

m∠B + 50° + 65° = 180°

m∠B = 180° - (50° + 65°) = 180° - 115° = 65°.  ⇒(1)

The sum of adjacent angles forming a straight line is also 180°.

m∠2 + 50° + 65° = 180°

m∠2 = 180° - (50° + 65°) = 180° - 115° = 65° ⇒(2)

From (1) and (2)

∴ m∠B = m∠2  = 65°

So, The angles B and 2 are congruent.

Answer 2

Angles B and 2 are congruent and the measure of angles is 65 degrees.

Given information:

A triangle has angle measures 50 degrees, 65 degrees, and angle B.

Two intersecting lines are extended to form three angles with a horizontal line. The measure of angles formed is 50 degrees, 65 degrees, and angle 2.

Now, the angles formed by two lines with the horizontal will result in a triangle.

The sum of all three interior angles of a triangle is 180 degrees. (Angle sum property)

So, the measure of angle 2 will be,

$\angle 2+50+65=180\\\angle 2=180-115\\\angle 2=65^{\circ}$

Similarly, the measure of angle B will be calculated as,

$\angle B+50+65=180\\\angle B=180-115\\\angle B=65^{\circ}$

Therefore, angles B and 2 are congruent and the measure of angles is 65 degrees.

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https://brainly.com/question/16903368