Question

Find the values of x, y, and z. The diagram is not to scale.​

Answer 1

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:

• 36° and 63°

Hence z = 36° +63°

• <z = 99°

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!