From DIAGRAM I, If, f = 60° and c = 8x − 4, find the value of x. If, e = 110 find the value of a,b,c,d,f,g and h

Angles $c$ and $f$ are alternate interior angles. Since the lines are parallel, alternate interior angles are equal.

$$c = f$$

Given $f = 60^\circ$ and $c = 8x - 4$.

$$8x - 4 = 60$$

Add 4 to both sides:

$$8x = 60 + 4$$ $$8x = 64$$

Divide by 8:

$$x = \frac{64}{8}$$ $$x = 8$$

The value of $x$ is $\boxed{8}$.

Angles $e$ and $f$ are angles on a straight line, so their sum is $180^\circ$.

$$e + f = 180^\circ$$ $$110^\circ + f = 180^\circ$$ $$f = 180^\circ - 110^\circ$$ $$f = 70^\circ$$

• $e$ and $h$ are vertically opposite angles:

$$h = e = 110^\circ$$

• $f$ and $g$ are vertically opposite angles:

$$g = f = 70^\circ$$

• $a$ and $e$ are corresponding angles:

$$a = e = 110^\circ$$

• $b$ and $f$ are corresponding angles:

$$b = f = 70^\circ$$

• $c$ and $g$ are corresponding angles:

$$c = g = 70^\circ$$

• $d$ and $h$ are corresponding angles:

$$d = h = 110^\circ$$

The values are: $a = \boxed{110^\circ}$ $b = \boxed{70^\circ}$ $c = \boxed{70^\circ}$ $d = \boxed{110^\circ}$ $f = \boxed{70^\circ}$ $g = \boxed{70^\circ}$ $h = \boxed{110^\circ}$