Given: ∆abc is isosceles m∠acb = 120° m ∈ ab , cm = 12 m∠bmc = 60° find: ab

Look at the picture.

This is isosceles triangle. Therefore, the angles at the base are congruent.

m∠ BAC = m∠ABC.

We know, the sum of the measures of the angles in a triangle is equal 180°.

Therefore:

m∠BAC + m∠ABC + m∠ACB = 180°

2m∠ABC + 120° = 180°     subtract 120° from both sides

2m∠ABC = 60°     divide both sides by 2

m∠ABC = 30°

m∠MCB = 90° → ΔMCB is a right triangle (30 - 60 - 90).

The sides of that triangle are in proportion: 1 : √3 : 2.

Therefore MC : BC : MB = 1 : √3 : 2

MC = 12 → BC = 12√3 and MB = 2 · 12 = 24

ΔCDB is the right triangle (30 - 60 - 90) too.

Therefore CD : BD : BC = 1 : √3 : 2

CD = 1/2 BC → CD = 1/2(12√3) = 6√3

BD = CD√3 → BD = 6√3(√3) = 6(3) = 18

AB = 2BD therefore your answer is:

b. x + 1

step-by-step explanation:

i'am smart

no association

step-by-step explanation:

if you have eyes and you can use them efficiently you can see that it just looks like random dots like do a line of best fit and like they're so spread out it's such a weak association you might as well consider it nonexistent