Question

1. 28° 29° 65° x y z y = ____

Explanation:

Step1: Find angle in left - hand triangle

In the left - hand triangle, using the angle - sum property of a triangle ($180^{\circ}$ in a triangle). Let the third angle be $a$. So $a=180^{\circ}-(28^{\circ}+65^{\circ})=87^{\circ}$.

Step2: Find $x$

Since the two angles $a$ and the angle adjacent to it (formed by the line dividing the large triangle) are supplementary, and the adjacent angle is $180^{\circ}-a = 93^{\circ}$. In the right - hand small triangle, using the angle - sum property again. We know one angle is $29^{\circ}$. Let's find $x$. The third angle in the right - hand small triangle (adjacent to $z$) is $180^{\circ}-(93^{\circ}+29^{\circ}) = 58^{\circ}$. Then $x = 180^{\circ}-(93^{\circ}+29^{\circ})=58^{\circ}$.

Step3: Find $y$

In the right - hand small triangle, we know one angle is $29^{\circ}$ and we just found the other non - $y$ angle is $58^{\circ}$. Using the angle - sum property of a triangle, $y=180^{\circ}-(29^{\circ}+58^{\circ}) = 93^{\circ}$.

Answer:

$93^{\circ}$