In triangle abc, m∠abc = (4x – 12)° and m∠acb = (2x + 26)°. yin says that if x = 19, the triangle must be equilateral. is he correct? justify your answer

No, Yin is not correct. If  x = 19, the measure of angle ABC = 4(19) – 12 = 64. Therefore, the two base angles measure 64°. An equilateral triangle is equiangular, so each angle would have to measure 60° because there are 180° in a triangle.

Yin is incorrect because when the value of x is 19 both the angles is equal to but in equilateral triangle all the angles must be equal to and this can be determine by using the properties of equilateral triangle.

Given :

In triangle ABC, ABC = (4x – 12)° and ACB = (2x + 26)°.

In equilateral triangle all the three sides of the triangle are equal and all the interior angles are congruent to each other and equal to .

So, to prove that the given triangle ABC is an equilateral triangle than both the given angles must be equal to .

= 76 - 12

=

= 38 + 26

=

Therefore, Yin is incorrect because when the value of x is 19 both the angles is equal to but in equilateral triangle all the angles must be equal to .

For more information, refer the link given below:

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300pi

step-by-step explanation:

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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