Question

unit i exam on lessons 1.1 to 1.12 (33 points possible)
part 2: free response questions: directions: show all of your work. an answer with no work will receive one point. you may earn partial credit for each question.

1. (3 points) in the accompanying diagram, ∠abc is a straight angle, m∠abd=(x + 42)°, and m∠dbc = 63°. find the value of x.

Explanation:

Step1: Recall straight - angle property

A straight angle $\angle ABC$ has a measure of $180^{\circ}$. So, $m\angle ABD+m\angle DBC = 180^{\circ}$.

Step2: Substitute given angle measures

We know that $m\angle ABD=(x + 42)^{\circ}$ and $m\angle DBC = 63^{\circ}$. Substituting these into the equation from Step 1 gives $(x + 42)+63=180$.

Step3: Simplify the left - hand side

$x+42 + 63=x + 105$. So the equation becomes $x+105 = 180$.

Step4: Solve for x

Subtract 105 from both sides of the equation: $x=180 - 105$.
$x = 75$.

Answer:

$x = 75$