Question

select all the true statements given the figure below.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(m\angle4=m\angle1 + m\angle2\).

Step2: Use the linear pair property

Since \(\angle3\) and \(\angle4\) form a linear pair (they are adjacent and supplementary), \(m\angle4=180 - m\angle3\) (because \(m\angle3+m\angle4 = 180^{\circ}\), so \(m\angle4=180 - m\angle3\) by subtracting \(m\angle3\) from both sides of the equation \(m\angle3 + m\angle4=180^{\circ}\)).

Answer:

\(m\angle4 = m\angle1 + m\angle2\), \(m\angle4=180 - m\angle3\)