Question

In the figure below, m ZABD=85°, and m2 2 is four times m2 1. Find m2 1.АmZ1 = 0C С2.В.D

Answer 1

According to the given problem,

`\begin{gathered} \angle2=2\angle1 \\ \angle ABD=85^(\circ) \end{gathered}`

From the diagram, it is observed that the angles 1 and angle 2, together constitute the angle ABD.

Therefore it follows that,

`\angle ABD=\angle1+\angle2`

Substitute the values and simplify the equation obtained,

`\begin{gathered} 85=\angle1+2\angle1 \\ 3\angle1=85 \\ \angle1=(85)/(3) \\ \angle1\approx28.33^(\circ) \end{gathered}`

Thus, the angle 1 measures approximately 28.33 degrees.