Question

1. find the measure of ∠abd and ∠dbc given m∠abc = 140°. 4x - 8 3x + 8

Explanation:

Step1: Set up an equation

Since $\angle ABC=\angle ABD+\angle DBC$, we have $(4x - 8)+(3x + 8)=140$.
Simplifying the left - hand side gives $4x-8 + 3x+8=7x$. So, $7x = 140$.

Step2: Solve for x

Dividing both sides of the equation $7x = 140$ by 7, we get $x=\frac{140}{7}=20$.

Step3: Find $\angle ABD$

Substitute $x = 20$ into the expression for $\angle ABD$, which is $4x-8$. So, $\angle ABD=4\times20 - 8=80 - 8=72^{\circ}$.

Step4: Find $\angle DBC$

Substitute $x = 20$ into the expression for $\angle DBC$, which is $3x + 8$. So, $\angle DBC=3\times20+8=60 + 8=68^{\circ}$.

Answer:

$\angle ABD = 72^{\circ}$, $\angle DBC=68^{\circ}$