Question

angles cad and bad form a linear pair, shown below. if the m∠cad=(3x + 46)° and m∠bad=(4z + 15)°, then the value of z is, the m∠cad =, and the m∠bad =

Explanation:

Step1: Recall linear - pair property

Linear - pair of angles sum to 180°. So, \(m\angle CAD+m\angle BAD = 180^{\circ}\).
\((3x + 46)+(4x+15)=180\)

Step2: Combine like - terms

\(3x+4x+46 + 15=180\), which simplifies to \(7x+61 = 180\).

Step3: Isolate the variable term

Subtract 61 from both sides: \(7x=180 - 61\), so \(7x=119\).

Step4: Solve for x

Divide both sides by 7: \(x=\frac{119}{7}=17\).

Step5: Find \(m\angle CAD\)

Substitute \(x = 17\) into the expression for \(m\angle CAD\): \(m\angle CAD=3x + 46=3\times17+46=51 + 46=97^{\circ}\).

Step6: Find \(m\angle BAD\)

Substitute \(x = 17\) into the expression for \(m\angle BAD\): \(m\angle BAD=4x+15=4\times17+15=68 + 15=83^{\circ}\).

Answer:

The value of \(x\) is 17, \(m\angle CAD = 97^{\circ}\), and \(m\angle BAD=83^{\circ}\).