Question

what is the value of t?

Explanation:

Step1: Use the property of straight - line angles

The sum of angles on a straight line is \(180^{\circ}\). Let's assume the three angles (\(27^{\circ}\), \(t\), and the angle which is vertical to \(78^{\circ}\)) form a straight line. Since vertical angles are equal, the angle vertical to \(78^{\circ}\) is \(78^{\circ}\).
So, \(27 + t+78=180\).

Step2: Solve the equation for \(t\)

First, simplify the left - hand side of the equation: \(27 + 78+t=180\), which gives \(105 + t=180\).
Then, subtract \(105\) from both sides of the equation: \(t=180 - 105\).

Answer:

\(75\)