Answer:
[tex]\angle F =\bold{88^\circ}[/tex]
Step-by-step explanation:
Given a [tex]\triangle FGH[/tex] with the following angles:
[tex]\text{m}\angle F = (6x-14)^{\circ}[/tex]
[tex]\text{m}\angle G = (4x-8)^{\circ}[/tex]
[tex]\text{m}\angle H = (x+15)^{\circ}[/tex]
To find:
[tex]\text{m}\angle F[/tex] = ?
Solution:
Here, we can simply use the angle sum property of a triangle to find the value of [tex]\text{m}\angle F[/tex].
As per the angle sum property of a triangle, the sum of all the interior angles a triangle is equal to [tex]180^\circ[/tex].
[tex]\angle F + \angle G + \angle H = 180^\circ[/tex]
Putting all the given values in the above equation, we get:
[tex](6x-14)^{\circ} + (4x-8)^{\circ} + (x+15)^{\circ} = 180^\circ\\\Rightarrow 11x-7=180^\circ\\\Rightarrow 11x=180+7\\\Rightarrow 11x=187\\\Rightarrow x = \bold{17}[/tex]
Putting the value of [tex]x[/tex] in [tex]\angle F[/tex]
[tex]\text{m}\angle F = (6x-14)^\circ\\\Rightarrow \text{m}\angle F = (6\times 17-14)^\circ\\\Rightarrow \text{m}\angle F = \bold{88^\circ}[/tex]
