Question

algebra find each missing angle measure. 17. 18. 19.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Calculate angle 1 for question 17

Let the missing angle be \(x\). We know two angles of the triangle are 60° and 63°. So, \(x = 180-(60 + 63)\).
\[x=180 - 123=57^{\circ}\]

Step3: For question 18

The exterior - angle property states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let the missing angle be \(y\). The exterior angle is 128.5° and one non - adjacent interior angle is 13°. So, \(y=128.5 - 13\).
\[y = 115.5^{\circ}\]

Step4: For question 19

First, find the third interior angle of the triangle. Let the third interior angle be \(z\). Using the angle - sum property of a triangle (\(z=180-(45 + 47)\)), \(z = 180-92 = 88^{\circ}\). Angle 3 is a straight - line angle (180°) with the interior angle \(z\), so \(\angle3=180 - 88=92^{\circ}\). Angle 4 and the interior angle \(z\) are vertical angles, so \(\angle4 = 88^{\circ}\).

Answer:

1. \(57^{\circ}\); 18. \(115.5^{\circ}\); 19. \(\angle3 = 92^{\circ}\), \(\angle4 = 88^{\circ}\)