Question

dition postulate to find a missing angle. 11. given: ∠bac = 2x + 11 ∠cad = x + 13 m∠bad = 60° find: m∠bac

Explanation:

Step1: Apply angle - addition postulate

By the angle - addition postulate, $\angle BAC+\angle CAD=\angle BAD$. Substitute the given expressions: $(2x + 11)+(x + 13)=60$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side: $2x+x+11 + 13=60$, which simplifies to $3x+24 = 60$.

Step3: Solve for $x$

Subtract 24 from both sides of the equation: $3x=60 - 24$, so $3x=36$. Then divide both sides by 3: $x = 12$.

Step4: Find $\angle BAC$

Substitute $x = 12$ into the expression for $\angle BAC$. $\angle BAC=2x + 11=2\times12+11$. Calculate $2\times12+11=24 + 11=35$.

Answer:

$m\angle BAC = 35^{\circ}$