Question

algebra find each missing angle measure. 17. 18. 128.5° 13° 19. 45° 3 4 47°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Also, for a linear - pair of angles, the sum of the two angles is 180°.

Step2: Solve for problem 17

Let the missing angle be \(x\). Given two angles of the triangle are 60° and 61°. Using the angle - sum property of a triangle \(x + 60+61 = 180\). Then \(x=180-(60 + 61)=180 - 121 = 59^{\circ}\).

Step3: Solve for problem 18

First, find the non - labeled interior angle adjacent to the 13° exterior angle. Let this angle be \(y\). Since \(y+13 = 180\) (linear pair), then \(y = 180 - 13=167^{\circ}\). Let the missing angle be \(z\). Using the angle - sum property of a triangle \(z+128.5 + 167=180\). Then \(z=180-(128.5 + 167)=180 - 295.5=- 115.5\) which is incorrect. We should use the exterior - angle property. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let the missing angle be \(z\). The exterior angle of the triangle is 128.5° and one non - adjacent interior angle is 13°. So \(z=128.5 - 13 = 115.5^{\circ}\).

Step4: Solve for problem 19

Let the missing angle be \(a\). Using the angle - sum property of a triangle \(a+45 + 47=180\). Then \(a=180-(45 + 47)=180 - 92 = 88^{\circ}\).

Answer:

1. \(59^{\circ}\); 18. \(115.5^{\circ}\); 19. \(88^{\circ}\)