Question

6b. ray ab bisects ∠dac. solve for x. 6c. ray zx bisects ∠wxy. find m∠wxz if m∠wxy = 82°. 7b. solve for x. 7c. solve for x.

Explanation:

6B

Step1: Identify angle bisector property

Since \( AB \) bisects \( \angle DAC \) and \( \angle DAC = 90^\circ \) (right angle), then \( \angle DAB=\angle BAC = \frac{90^\circ}{2}=45^\circ \). So \( 7x - 4 = 45 \).

Step2: Solve for \( x \)

Add 4 to both sides: \( 7x=45 + 4=49 \).
Divide by 7: \( x=\frac{49}{7}=7 \).

Step1: Apply angle bisector definition

If \( ZX \) bisects \( \angle WXY \), then \( m\angle WXZ=\frac{1}{2}m\angle WXY \).

Step2: Substitute the given angle

Given \( m\angle WXY = 82^\circ \), so \( m\angle WXZ=\frac{82^\circ}{2}=41^\circ \).

Step1: Recognize right angle sum

The two angles \( 8x + 5^\circ \) and \( 3x + 8^\circ \) form a right angle (\( 90^\circ \)), so \( (8x + 5)+(3x + 8)=90 \).

Step2: Simplify and solve

Combine like terms: \( 11x+13 = 90 \).
Subtract 13: \( 11x=90 - 13 = 77 \).
Divide by 11: \( x=\frac{77}{11}=7 \).

Answer:

\( x = 7 \)

6C