Question

7)
$x = 180 - 115 = 65$
$165 + 65 = 105$
$1430 = 18$
$x = 65$
$65 - 65 = 50$
$y = 50^{circ}$
$z = 65$

Explanation:

Step1: Find x using linear pair

A linear pair of angles sums to \(180^\circ\). So, \(x + 115^\circ=180^\circ\).
\(x = 180^\circ - 115^\circ = 65^\circ\)

Step2: Identify triangle type (isosceles)

The triangle has two equal sides (marked with ticks), so it's isosceles. Thus, \(z = x = 65^\circ\) (base angles of isosceles triangle are equal).

Step3: Find y using triangle angle sum

Sum of angles in a triangle is \(180^\circ\). So, \(y + x+ z = 180^\circ\).
Substitute \(x = 65^\circ\) and \(z = 65^\circ\): \(y + 65^\circ+ 65^\circ = 180^\circ\)
\(y = 180^\circ-(65^\circ + 65^\circ)=180^\circ - 130^\circ = 50^\circ\)

Answer:

\(x = 65^\circ\), \(y = 50^\circ\), \(z = 65^\circ\) (Note: The original marking for \(z\) as wrong was incorrect; \(z\) should be \(65^\circ\) as shown in the steps.)