Question

what is the value of x? x = exterior angle = non - adjacent interior angle+non - adjacent interior angle 100° 70° x°

Explanation:

Step1: Apply exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(100^{\circ}+x^{\circ}=70^{\circ}+\text{third interior angle}\). Also, we know that the sum of interior angles of a triangle is \(180^{\circ}\). Let the third interior angle be \(y\). Then \(70^{\circ}+y + (180 - x)^{\circ}=180^{\circ}\), which simplifies to \(y=x - 70^{\circ}\). Using the exterior - angle property \(100 + x=70+(x - 70)\) is incorrect. The correct exterior - angle property application is \(x=100 - 70\).

Step2: Calculate the value of \(x\)

\(x = 30\)

Answer:

\(30\)