Question

use the diagram to solve for the angle measurement, given that ∠bae = 130°. 8. ∠bac 9. ∠cad 10. ∠dae

Explanation:

Step1: Set up an equation

Since $\angle BAE=\angle BAC+\angle CAD+\angle DAE$, we have $(3x - 10)+(2x + 5)+(x + 15)=130$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $(3x+2x + x)+(-10 + 5+15)=130$, which simplifies to $6x+10 = 130$.

Step3: Solve for x

Subtract 10 from both sides: $6x=130 - 10=120$. Then divide both sides by 6: $x=\frac{120}{6}=20$.

Step4: Find $\angle BAC$

Substitute $x = 20$ into the expression for $\angle BAC$: $\angle BAC=3x-10=3\times20 - 10=60 - 10 = 50^{\circ}$.

Step5: Find $\angle CAD$

Substitute $x = 20$ into the expression for $\angle CAD$: $\angle CAD=2x + 5=2\times20+5=40 + 5=45^{\circ}$.

Step6: Find $\angle DAE$

Substitute $x = 20$ into the expression for $\angle DAE$: $\angle DAE=x + 15=20+15=35^{\circ}$.

Answer:

1. $\angle BAC = 50^{\circ}$
2. $\angle CAD = 45^{\circ}$
3. $\angle DAE = 35^{\circ}$