Question

1. m∠xyz = 117°. find m∠xyw and m∠wyz.

(6x + 44)° (-10x + 65)°

Explanation:

Step1: Set up angle sum equation

The sum of $m\angle XYW$ and $m\angle WYZ$ equals $m\angle XYZ$.
$$(6x + 44) + (-10x + 65) = 117$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.
$$6x - 10x + 44 + 65 = 117$$
$$-4x + 109 = 117$$
$$-4x = 117 - 109$$
$$-4x = 8$$
$$x = \frac{8}{-4} = -2$$

Step3: Calculate $m\angle XYW$

Substitute $x=-2$ into the expression.
$$m\angle XYW = 6(-2) + 44 = -12 + 44 = 32$$

Step4: Calculate $m\angle WYZ$

Substitute $x=-2$ into the expression.
$$m\angle WYZ = -10(-2) + 65 = 20 + 65 = 85$$

Step5: Verify angle sum

Check if the sum equals $117^\circ$.
$$32 + 85 = 117$$

Answer:

$m\angle XYW = 32^\circ$, $m\angle WYZ = 85^\circ$