Question

Fond the degree measure of each angle in the triangle

Answer 1

Note that the sum of the angles in a triangle is always 180 degrees.

So it follows that :

$\angle F+\angle G+\angle H=180$

The triangle has a right angle at G, and a right angle measures 90 degrees.

angle F = 4x + 15

and

angle H = 3x + 12

Substitute the angle values to the formula and solve the value of x :

$\begin{gathered} \angle F+\angle G+\angle H=180 \\ (4x+15)+(90)+(3x+12)=180 \\ 7x+117=180 \\ 7x=180-117 \\ 7x=63 \\ x=\frac{63}{7}=9 \end{gathered}$

Now we have the value of x, substitute this value to the angles.

$\begin{gathered} F=4x+15=4(9)+15=51 \\ H=3x+12=3(9)+12=39 \end{gathered}$

Therefore, the angles are :

F = 51 degrees

G = 90 degrees

H = 39 degrees