Question

PLS HELP THIS IS URGENT!GIVING BRAINLIEST

Answer 1

The value of AB = 36

What is an isosceles triangle?

An isosceles triangle is a triangle with base angles equal with any two sides equal.

Analysis:

∠ACB = 120

ABC is isosceles, so ∠CAB = ∠CBA = x

x + x + 120 = 180 ( sum of angles in Δ ABC)

2x = 60

x = 30

∠AMC = 180 - ∠BMC( angles on a straight line)

           = 180 - 60 = 120

∠ACM = 180 - (30 + 120) = 180 - 150 = 30°

∠MCB = 90°

using sine rule,

12/sin 30 = AM/ sin 30

AM = 12

MB/sin 90 = 12/sin30

MB sin 30 = 12 sin 90

MB = 12/sin 30 = 12/0.5 = 24

AB = MB + AM = 24 + 12 = 36

Learn more about isosceles triangle: brainly.com/question/1475130

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Answer 2

Answer: 36

Step-by-step explanation:

$\overline{AB} \cong \overline{BC}$ (Triangle ABC is isosceles)

$m\angle CAB=m\angle CBA=30^{\circ}$ (base angles of an isosceles triangle are congruent)

$\angle MCB=90^{\circ}$ (In triangle CMB, angles in a triangle add to 180 degrees)

$\angle ACM=30^{\circ}$ (triangle sum theorem)

$MB=24$ (30-60-90 triangle CMB)

$AB=12$ (sides opposite congruent angles in a triangle are congruent)

$AB=36$ (segment addition postulate)