Question

bd→bieds ∠abc. find the indicated measure/value.

1. find x:
2. find ∠abd.
3. find ∠bdc.
4. find ∠abc.
5. find ∠abd
6. find ∠dbc.

Explanation:

Step1: Use the angle - bisector property

Since \(BD\) bisects \(\angle ABC\), then \(\angle ABD=\angle DBC\). For problem 47, we have \(2x + 7=4x-9\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(2x + 7-2x=4x-9 - 2x\), which gives \(7 = 2x-9\). Then add 9 to both sides: \(7 + 9=2x-9 + 9\), so \(16 = 2x\). Divide both sides by 2: \(x=\frac{16}{2}=8\).

Step3: Calculate \(\angle ABC\)

\(\angle ABC=(2x + 7)+(4x-9)\). Substitute \(x = 8\) into the expression: \(\angle ABC=(2\times8 + 7)+(4\times8-9)=(16 + 7)+(32-9)=23 + 23=46^{\circ}\)

Answer:

\(46^{\circ}\)