Question

1. in the accompanying diagram, $overleftrightarrow{ab}$ intersects $overleftrightarrow{pq}$ and $overleftrightarrow{rs}$ at c and d, respectively. if $overleftrightarrow{pq}paralleloverleftrightarrow{rs}$, $mangle rdb=(2x - 10)^{circ}$, and $mangle qca=(3x - 65)^{circ}$, find $x$.

Explanation:

Step1: Identify angle - relationship

Since $\overline{PQ}\parallel\overline{RS}$, $\angle RDB$ and $\angle QCA$ are corresponding angles, so $\angle RDB=\angle QCA$.

Step2: Set up the equation

Set up the equation $2x - 10=3x - 65$.

Step3: Solve the equation

Subtract $2x$ from both sides: $- 10=x - 65$.
Then add 65 to both sides: $x=55$.

Answer:

$x = 55$