given triangle ABC with MB equals 62 degrees and side AC extended to d as shown below which value of x makes a b congruent to CB

4) 121 degrees
because if x is 121 degrees then angle BCA will equal 59 degrees (the two angles must equal 180) so using the sum of a triangle's angles, then angle BAC will have to equal 59, making the triangle an isoceles, which will make AB to be congruent to BC.

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Abdulazeez10 Abdulazeez10 · Answer 2 · 2022-05-19T11:08:01+02:00

The value of x that makes AB congruent to CB is 121°. The correction option is 4) 121°

Calculating angles

From the question, we are to determine the value of x that makes AB congruent to CB

If AB is congruent to CB, then we get an isosceles triangle

Therefore,

m ∠A = m ∠C (Base angles of an isosceles triangle)

Also,

m∠A + m∠B + m∠C = 180° (Sum of angles in a triangle)

m∠A + 62° + m∠A = 180°

2 × m∠A = 180° - 62°

2 × m∠A = 118°

m∠A = 118° / 2

m∠A = 59°

∴ m∠A = m∠C = 59°

Now, to calculate x

x + m∠C = 180° (Sum of angles on a straight line)

x + 59° = 180°

x = 180° - 59°

x = 121°

Hence, the value of x that makes AB congruent to CB is 121°. The correction option is 4) 121°

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