Answer:
x = 81°
y = 68°
z = 99°
Explanation:
We know the exterior angle property of triangle, which says:
- The angle exterior to the triangle is equal to the sum of opposite two interior angles.
Hence here we can see < z makes exterior angle to the first triangle, also the opposite two interior angle of < z has been given:
Hence z = 36° +63°
Also, < x and < z lie on the same straight line, i.e. they obey linear pair theorem.
- Their sum must be equal to 180°(According to the theorem)
So <(z + x) = 180°
- 99° + x° = 180°
- x = 180° -99°
- x° = 81°
Similar to < z, < x makes exterior angle to the opposite two interior angles of 13° and y°, hence we can say:
- x° = 13° + y°
- 81° = 13° + y°
- y = 81° -13°
- y = 68°
I used laws of triangle instead of using angle sum property to make it interesting!