Question

In AOPQ, mZO = (6x – 14)°, mZP = (2x + 16)°, and mZQ = (2x + 8)°. Find mZQ.

Answer 1

`\measuredangle Q=42`

Step-by-step explanation

Step 1

the sum of the internal angles in a triangle equals 18o, so

`\begin{gathered} (2x+16)+(6x-14)+(2x+8)=180 \\ 2x+16+6x-14+2x+8=180 \\ \text{add similar terms} \\ 10x+10=180 \\ \text{subtract 10 in both sides} \\ 10x+10-10=180-10 \\ 10x=170 \\ \text{divide both sides by 10} \\ (10x)/(10)=(170)/(10) \\ x=17 \end{gathered}`

Step 2

now, replace the value of x in angle Q to find it

`\begin{gathered} \measuredangle Q=(2x+8) \\ \measuredangle Q=(2\cdot17+8) \\ \measuredangle Q=(34+8) \\ \measuredangle Q=42 \end{gathered}`

I hope this helps you