Question

which of the following equations could be used to find the missing angle measure?
29 + 45 = q
180 - q = 29 + 45
q + 90 = 29 + 45
none of these

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.
In the given triangle, the exterior angle is \(q^{\circ}\), and the two non - adjacent interior angles are \(29^{\circ}\) and \(45^{\circ}\).
So, \(q = 29+45\)

Step2: Analyze each option

• Option 1: \(29 + 45=q\) is correct according to the exterior angle theorem.
• Option 2: \(180 - q=29 + 45\) is based on the linear pair ( \(q+(180 - q)=180\) and the sum of interior angles of a triangle \(29 + 45+(180 - q)=180\)), but this is not the direct equation for finding \(q\) using the exterior angle theorem.
• Option 3: \(q + 90=29+45\) is incorrect as there is no \(90^{\circ}\) angle relationship given in the problem.

Answer:

\(29 + 45=q\)