Question

in △def, m∠d = 35° and m∠f = 88°. what is m∠e?
a. 53°
b. 123°
c. 57°
d. 237°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, in \(\triangle DEF\), \(m\angle D+m\angle E + m\angle F=180^{\circ}\).

Step2: Solve for \(m\angle E\)

We know \(m\angle D = 35^{\circ}\) and \(m\angle F=88^{\circ}\). Substitute these values into the equation: \(m\angle E=180^{\circ}-m\angle D - m\angle F\). Then \(m\angle E=180^{\circ}-35^{\circ}-88^{\circ}\). First, \(180 - 35=145^{\circ}\), and then \(145 - 88 = 57^{\circ}\).

Answer:

C. \(57^{\circ}\)