Question

1. find the values of w, x, y and z.
2. if c || d and a || b, determine if the following statement

a ∠10 ≅ ∠15
b ∠1 ≅ ∠4
c m∠16 + m∠14 = 180°
d ∠7 ≅ ∠14
e m∠10 + m∠3 = 180°

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. Since the angle of $72^{\circ}$ and $w$ are vertical angles, $w = 72$.

Step2: Identify corresponding - angle relationship

Corresponding angles formed by parallel lines $m$ and $n$ are equal. The $72^{\circ}$ angle and $y$ are corresponding angles, so $y=72$.

Step3: Solve for $x$

The angle $12x^{\circ}$ and the $72^{\circ}$ angle are vertical angles. So we set up the equation $12x = 72$. Dividing both sides by 12 gives $x=\frac{72}{12}=6$.

Step4: Solve for $z$

The angle $z$ and the $72^{\circ}$ angle are supplementary (linear - pair). So $z + 72=180$, then $z=180 - 72 = 108$.

Answer:

$w = 72$, $x = 6$, $y = 72$, $z = 108$