Question

retake geometry: angles and proofs test name:

1. complete a two - column proof:

given: bd bisects < abc
prove: < dbc = 44

1. complete a two - column proof:

given: < cea and < ceb are supplementary.
prove: x = 40

Explanation:

Step1: Use the angle - bisector definition

Since \(BD\) bisects \(\angle ABC\), then \(\angle ABD=\angle DBC\). So \(6x + 14=3x+29\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(6x-3x + 14=3x-3x + 29\), which gives \(3x+14 = 29\).
Subtract \(14\) from both sides: \(3x+14-14=29 - 14\), so \(3x=15\).
Divide both sides by \(3\): \(x = 5\).

Step3: Find \(\angle DBC\)

Substitute \(x = 5\) into the expression for \(\angle DBC\) (\(3x + 29\)).
\(\angle DBC=3\times5+29=15 + 29=44\)

Answer:

The proof is completed as above, and we have shown that \(\angle DBC = 44\)