Direct answer :
[tex] \color{plum} \: x \: \bold{ \tt \: = \: 11}[/tex]
Steps to derive the correct answer :
Given :
- segment AB = segment DE
- segment BC = segment EF
- segment AC = segment DF
Since all sides are equal triangle ABC is congruent to triangle DEF under the SSS congruence criterion.
m∠B = (92+y)°
m∠E = (6y-28)°
We know that :
Which means :
[tex] = \tt92 + y = 6y - 28[/tex]
[tex] =\tt 92 = 6y - 28 - y[/tex]
[tex] =\tt 92 = 5y - 28[/tex]
[tex] = \tt92 + 28 = 5y[/tex]
[tex] = \tt120 = 5y[/tex]
[tex] =\tt y = \frac{120}{5} [/tex]
[tex] =\tt y = 24[/tex]
Thus, the value of y = 24
Then :
angle B :
[tex] =\tt 92 + y[/tex]
[tex] =\tt 92 + 24[/tex]
[tex] = \tt116[/tex]
Thus, the measure of angle B = 116
angle E :
[tex] = \tt6y - 28[/tex]
[tex] =\tt 6 \times 24 - 28[/tex]
[tex] =\tt 144 - 28[/tex]
[tex] =\tt 116[/tex]
Thus, the measure of angle E = 116
Since the measure of both these angles is equal we can conclude that we have found out their correct measures.
measure of segment AC = 2x + 47
Measure of segment DF = 6x + 3
Which means :
[tex] = \tt6x + 3 = 2x + 47[/tex]
[tex] = \tt6x + 3 - 2x = 47[/tex]
[tex] = \tt4x + 3 = 47[/tex]
[tex] \tt4x = 47 - 3 \\ 4x = 44[/tex]
[tex] =\tt x = \frac{44}{4} [/tex]
[tex] =\tt x = 11[/tex]
Thus, the value of x = 11
Let us check whether or not we have found out the correct value of x by placing 11 in the place of x :
[tex] = \tt6 \times 11 + 3 = 11 \times 2 + 47[/tex]
[tex] =\tt 66 + 3 = 22 + 47[/tex]
[tex] =\tt 69 = 69[/tex]
Therefore, the value of x = 11
