Question

complete the statements about the relationship between the two labeled angles.
given: ( mangle udr = 63^circ )
the two labeled angles are adjacent angles.
that means that their measures sum to ( 63^circ ).
use the relationship you determined to write an equation to help you solve for ( x ).
( 9x + 5x = 63 )
solve for ( x ). write your answer as an integer or decimal.
( 9x + 5x = 63 )
multiply both sides : multiply both sides by what?
( 14x \times square = 63 \times square )
hint: the coefficient is 14. what value can you multiply both sides of the equation by so that the coefficient becomes 1?

Explanation:

Step1: Simplify the left side

First, we combine like terms in the equation \(9x + 5x = 63\). Combining \(9x\) and \(5x\) gives \(14x\), so the equation becomes \(14x = 63\).

Step2: Solve for x

To solve for \(x\), we need to isolate \(x\). We do this by dividing both sides of the equation \(14x = 63\) by 14. So we multiply both sides by \(\frac{1}{14}\) (which is the same as dividing by 14).
\[14x\times\frac{1}{14}=63\times\frac{1}{14}\]
Simplifying the left side, \(14x\times\frac{1}{14}=x\). On the right side, \(63\times\frac{1}{14}=\frac{63}{14} = 4.5\).

Answer:

The value to multiply both sides by is \(\frac{1}{14}\) (or \(0.0714\) approximately, but as a fraction \(\frac{1}{14}\) is exact). So filling in the boxes, we have \(14x\times\boldsymbol{\frac{1}{14}} = 63\times\boldsymbol{\frac{1}{14}}\) and \(x=\frac{63}{14} = 4.5\). The value of \(x\) is \(4.5\).