Question

1. angle addition postulate worksheet

a. use the following diagram and the angle addition postulate to solve for the value of x.
b. if m∠xyz = 10x - 15 and m∠zyw = 6x + 12, and m∠xyw = 99, find x.
c. if m∠pqr = x + 10, m∠rqs = 2x + 5, and m∠pqs = 69, find x.

Explanation:

Step1: Apply angle - addition postulate

According to the angle - addition postulate, the sum of adjacent angles equals the larger angle. In part a, $\angle BAC+\angle CAD = 90^{\circ}$ (since $\angle BAD = 90^{\circ}$), so $(13x + 30)+(2x+15)=90$.
Combine like - terms: $13x+2x+30 + 15=90$, which simplifies to $15x+45 = 90$.

Step2: Solve for x

Subtract 45 from both sides: $15x=90 - 45$, so $15x=45$.
Divide both sides by 15: $x=\frac{45}{15}=3$.

In part b, $\angle XYZ+\angle ZYW=\angle XYW$. So, $(10x - 15)+(6x + 12)=99$.
Combine like - terms: $10x+6x-15 + 12=99$, which simplifies to $16x-3 = 99$.
Add 3 to both sides: $16x=99 + 3=102$.
Divide both sides by 16: $x=\frac{102}{16}=\frac{51}{8}=6.375$.

In part c, $\angle PQR+\angle RQS=\angle PQS$. So, $(x + 10)+(2x + 5)=69$.
Combine like - terms: $x+2x+10 + 5=69$, which simplifies to $3x+15 = 69$.
Subtract 15 from both sides: $3x=69 - 15=54$.
Divide both sides by 3: $x = 18$.

Answer:

a. $x = 3$
b. $x=6.375$
c. $x = 18$