Question

that means that their measures sum to 56°. use the relationship you determined to write an equation to help you solve for x. (6x - 15)° 23°

Explanation:

Step1: Identify the angle sum relationship

The two angles at point \( B \) ( \( 23^\circ \) and \( (6x - 15)^\circ \)) sum up to \( 56^\circ \). So we can write the equation by adding the two angle measures and setting it equal to \( 56^\circ \).
\( 23+(6x - 15)=56 \)

Step2: Simplify the left - hand side

First, simplify \( 23+(6x - 15) \). Combine the constant terms: \( 23-15 + 6x=8 + 6x \). So the equation becomes \( 6x+8 = 56 \).

Step3: Solve for \( x \)

Subtract 8 from both sides of the equation: \( 6x+8 - 8=56 - 8 \), which simplifies to \( 6x = 48 \). Then divide both sides by 6: \( \frac{6x}{6}=\frac{48}{6} \), so \( x = 8 \).

Answer:

The value of \( x \) is \( 8 \). The equation to solve for \( x \) is \( 23+(6x - 15)=56 \) (or its simplified forms like \( 6x + 8=56 \)).