Question

use the diagram to solve for the angle measurement, given that ∠bae = 59°. 5. ∠bac 6. ∠cad 7. ∠dae (4x - 20)° (x + 12)° (x + 1)°

Explanation:

Step1: Set up an equation based on angle - sum

Since $\angle BAE=\angle BAC+\angle CAD+\angle DAE$, we have $(4x - 20)+(x + 12)+(x + 1)=59$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms on the left - hand side gives $(4x+x+x)+(-20 + 12+1)=59$, which simplifies to $6x-7 = 59$.

Step3: Solve for $x$

Add 7 to both sides of the equation: $6x-7 + 7=59 + 7$, so $6x=66$. Then divide both sides by 6: $x=\frac{66}{6}=11$.

Step4: Find $\angle BAC$

Substitute $x = 11$ into the expression for $\angle BAC$: $\angle BAC=4x-20=4\times11-20=44 - 20=24^{\circ}$.

Step5: Find $\angle CAD$

Substitute $x = 11$ into the expression for $\angle CAD$: $\angle CAD=x + 12=11+12=23^{\circ}$.

Step6: Find $\angle DAE$

Substitute $x = 11$ into the expression for $\angle DAE$: $\angle DAE=x + 1=11+1=12^{\circ}$.

Answer:

1. $\angle BAC = 24^{\circ}$
2. $\angle CAD = 23^{\circ}$
3. $\angle DAE = 12^{\circ}$