Question

1. what are the measures of the missing angles? ( m angle z = ) _ ( ^ { circ } ) 6. what is the measure of angle 1? ( m angle 1 = ) _ ( ^ { circ } )

Explanation:

Step1: Use the triangle angle - sum property

The sum of angles in a triangle is \(180^{\circ}\). For the triangle with angles \(z\), \(84^{\circ}\), and \(50^{\circ}\), we have \(z + 84+50=180\).

Step2: Solve for \(z\)

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Step3: Use the exterior - angle property for the second problem

The exterior - angle property states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the second triangle, if the two non - adjacent interior angles are \(61^{\circ}\) and \(50^{\circ}\), and the exterior angle is \(\angle1\). Then \(\angle1=61 + 50\).

Step4: Calculate \(\angle1\)

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Answer:

\(m\angle z = 46^{\circ}\), \(m\angle1=111^{\circ}\)