Question

the figure shows a triangle with an exterior angle at each vertex.
what is the value of y?
use the number pad to enter your answer in the box.
y =

Explanation:

Step1: Find interior angles from exteriors

The sum of an exterior angle and its adjacent interior angle is \(180^\circ\). So, the interior angles adjacent to \(141^\circ\) and \(127^\circ\) are \(180 - 141 = 39^\circ\) and \(180 - 127 = 53^\circ\) respectively.

Step2: Use triangle angle sum property

The sum of interior angles of a triangle is \(180^\circ\). Let the third interior angle be \(8y^\circ\). So, \(39 + 53 + 8y = 180\).
Simplify: \(92 + 8y = 180\).
Subtract 92: \(8y = 180 - 92 = 88\).
Divide by 8: \(y = \frac{88}{8} = 11\).

Answer:

\(11\)