Question

Given the following diagram, find the missing measure. 2 VAN m 24 = 2x®, m 2 = (4/3)X, m_3 = 20°, find x. O 10 20 30 60

Answer 1

We know the angles in a triangle sum to 180 degrees. Thus, we can write:

`\angle1+\angle2+\angle3=180`

Also, we know straight line is 180 degrees. Thus we can write:

`\angle1+\angle4=180`

Putting these 2 equations together, we have:

`\begin{gathered} 180=180 \\ \angle1+\angle2+\angle3=\angle1+\angle4 \\ \therefore\angle2+\angle3=\angle4 \end{gathered}`

Now, we substitute the known expressions for the angles and solve for x:

`\begin{gathered} \angle2+\angle3=\angle4 \\ (4)/(3)x+20=2x \\ 2x-(4)/(3)x=20 \\ (2)/(3)x=20 \\ x=(20)/((2)/(3)) \\ x=20*(3)/(2) \\ x=30 \end{gathered}`