Question

find the value of x. then, find the measure of each labeled angle #7 (5x - 8)° (3x + 4)° x = __ (3x + 4)° = ° (5x - 8)° = __°

Explanation:

Step1: Set up equation

Since the two angles $(5x - 8)^{\circ}$ and $(3x + 4)^{\circ}$ are supplementary (sum to 180°), we have the equation $5x-8 + 3x + 4=180$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms, we get $(5x+3x)+(-8 + 4)=180$, which simplifies to $8x-4 = 180$.

Step3: Isolate the variable term

Add 4 to both sides of the equation: $8x-4 + 4=180 + 4$, resulting in $8x=184$.

Step4: Solve for x

Divide both sides by 8: $x=\frac{184}{8}=23$.

Step5: Find the measure of $(3x + 4)^{\circ}$

Substitute $x = 23$ into $3x + 4$: $3\times23+4=69 + 4=73$.

Step6: Find the measure of $(5x - 8)^{\circ}$

Substitute $x = 23$ into $5x - 8$: $5\times23-8=115 - 8=107$.

Answer:

$x = 23$
$(3x + 4)^{\circ}=73^{\circ}$
$(5x - 8)^{\circ}=107^{\circ}$