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 for part a

According to the angle - addition postulate, \((2x + 15)+(13x+30)=90\) (since \(\angle BAE = 90^{\circ}\)). Combine like - terms: \(2x+13x+15 + 30=90\), which simplifies to \(15x+45 = 90\).

Step2: Solve the equation for part a

Subtract 45 from both sides: \(15x=90 - 45\), so \(15x=45\). Then divide both sides by 15: \(x=\frac{45}{15}=3\).

Step3: Apply angle - addition postulate for part b

By the angle - addition postulate, \(m\angle XYZ+m\angle ZYW=m\angle XYW\). So \((10x - 15)+(6x + 12)=99\). Combine like - terms: \(10x+6x-15 + 12=99\), which gives \(16x-3 = 99\).

Step4: Solve the equation for part b

Add 3 to both sides: \(16x=99 + 3=102\). Then divide both sides by 16: \(x=\frac{102}{16}=\frac{51}{8}=6.375\).

Step5: Apply angle - addition postulate for part c

According to the angle - addition postulate, \(m\angle PQR+m\angle RQS=m\angle PQS\). So \((x + 10)+(2x + 5)=69\). Combine like - terms: \(x+2x+10 + 5=69\), which simplifies to \(3x+15 = 69\).

Step6: Solve the equation for part c

Subtract 15 from both sides: \(3x=69 - 15=54\). Then divide both sides by 3: \(x = 18\).

Answer:

a. \(x = 3\)
b. \(x=6.375\)
c. \(x = 18\)