In ΔFGH, \text{m}\angle F = (6x-14)^{\circ}m∠F=(6x−14) ∘ , \text{m}\angle G = (4x-8)^{\circ}m∠G=(4x−8) ∘ , and \text{m}\angle H = (x+15)^{\circ}m∠H=(x+15) ∘ . Find \text{m}\angle F. M∠F.

Step-by-step explanation:

Given a with the following angles:

To find:

= ?

Solution:

Here, we can simply use the angle sum property of a triangle to find the value of .

As per the angle sum property of a triangle, the sum of all the interior angles a triangle is equal to .

Putting all the given values in the above equation, we get:

Putting the value of in

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4y < -4

we need to isolate y. we can do this by simply dividing both sides by 4.

4y ÷ 4 > -4 ÷ 4

simplify.

y > -1

5 - y > 0

once again, we need to isolate y, so we can start off by subtracting 5 from both sides.

5 - y - 5 > 0 - 5

simplify.

-y > -5

divide both sides by -1.

** remember that when dividing any side by a negative, you must switch the sign! **

-y ÷ -1 < -5 ÷ -1

simplify.

y < 5

~hope i ! ~