Question

if ( mangle a = 110 ) degrees and ( mangle b = 35 ) degrees, find ( mangle 1 ).

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
In \(\triangle ABC\), \(\angle1\) is an exterior angle. The two non - adjacent interior angles are \(\angle A\) and \(\angle B\).

Step2: Calculate \(m\angle1\)

We know that \(m\angle A = 110^{\circ}\) and \(m\angle B=35^{\circ}\).
By the exterior - angle theorem, \(m\angle1=m\angle A + m\angle B\).
Substitute the values: \(m\angle1=110^{\circ}+ 35^{\circ}\).
\(m\angle1 = 145^{\circ}\)

Answer:

E. 145 degrees