Question

additional details were added for this assignment.
in this diagram, ( mangle1 = 37^{circ} ) and ( mangle3 = 97^{circ} ).
select a response from each drop - down menu to correctly complete this sentence.
based on the exterior angle theorem, the ( mangle4=) choose...( ^{circ} )
because the sum of the choose...
choose...( ) is
choose...( ) and ( angle4 ) forms a linear pair with angle choose...

Explanation:

Step1: Apply 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. In this case, \(\angle4\) is an exterior angle of the triangle, and the two non - adjacent interior angles are \(\angle1\) and \(\angle3\).

$$m\angle4=m\angle1 + m\angle3$$

Step2: Substitute the given values

Given \(m\angle1 = 37^{\circ}\) and \(m\angle3=97^{\circ}\), substitute these values into the formula.

$$m\angle4=37^{\circ}+97^{\circ}$$

$$m\angle4 = 134^{\circ}$$

Answer:

\(134\)