Question

1. if (mangle abd = 79^{circ}), what are (mangle abc) and (mangle dbc?) ((5x + 4)^{circ}) ((8x - 3)^{circ})

Explanation:

Step1: Set up an equation based on angle - addition

Since $\angle ABC=\angle ABD+\angle DBC$, we have $(5x + 4)+(8x-3)=79$.
Combining like - terms, we get $13x + 1=79$.

Step2: Solve for $x$

Subtract 1 from both sides of the equation: $13x=79 - 1=78$.
Then divide both sides by 13: $x=\frac{78}{13}=6$.

Step3: Find $m\angle ABC$

Substitute $x = 6$ into the expression for $\angle ABC$ which is $8x-3$.
$m\angle ABC=8\times6 - 3=48-3 = 45^{\circ}$.

Step4: Find $m\angle DBC$

Substitute $x = 6$ into the expression for $\angle DBC$ which is $5x + 4$.
$m\angle DBC=5\times6+4=30 + 4=34^{\circ}$.

Answer:

$m\angle ABC = 45^{\circ}$, $m\angle DBC=34^{\circ}$