Question

string art string art is created by wrapping string around nails or wires to form patterns. use the string art pattern below to find the values of x, y, and z. 86° 26° 101°

Explanation:

Step1: Use angle - sum property of a triangle

In a triangle, the sum of interior angles is 180°. Consider the triangle with angles \(x\), \(86^{\circ}\), and \(26^{\circ}\). So, \(x + 86^{\circ}+26^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

\(x=180^{\circ}-(86^{\circ} + 26^{\circ})=180^{\circ}-112^{\circ}=68^{\circ}\).

Step3: Use linear - pair property

The angle adjacent to \(y\) and \(101^{\circ}\) form a linear pair. A linear pair of angles sums to 180°. So, \(y = 180^{\circ}-101^{\circ}=79^{\circ}\).

Step4: Use angle - sum property of a triangle again

Consider the large triangle formed by the outer - most strings. Let's use the fact that the sum of angles in a triangle is 180°. We know one angle is \(y = 79^{\circ}\) and another is \(26^{\circ}\). Let the third angle be \(z\). Also, we can use the fact that the non - adjacent interior angles of a triangle are related to the exterior angle.
We know that the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. If we consider the angle related to \(z\), we can also use the angle - sum property. \(z=180^{\circ}-(79^{\circ}+26^{\circ}) = 75^{\circ}\).

Answer:

\(x = 68^{\circ}\), \(y = 79^{\circ}\), \(z = 75^{\circ}\)