Answer:
x = 50°
y = 30°
z = 80°
Explanation:
This shape is made up of 2 larger intersecting triangles, which also forms a smaller triangle and a quadrilateral.
Looking at the larger triangle with angles y°, 60° and right angle:
Sum of interior angles of a triangle = 180°
⇒ y + 60 + 90 = 180
⇒ y = 30°
Looking at the larger triangle with angles z°, 40° and 60°:
Sum of interior angles of a triangle = 180°
⇒ z + 60 + 40 = 180
⇒ z = 80°
We can work out x in two different ways.
Method 1
The angle adjacent to the right angle is also a right angle, since angles on a straight line add up to 180°.
This means that the small triangle with angles x° and 40° is a right triangle.
Sum of interior angles of a triangle = 180°
⇒ x + 40 + 90 = 180
⇒ x = 50°
Method 2
Look at the quadrilateral that has been formed by the 2 intersecting larger triangles.
Sum of interior angles of a quadrilateral = 360°
⇒ z + 60 + 90 + unmarked angle = 360
⇒ 80 + 60 + 90 + unmarked angle = 360
⇒ unmarked angle = 130°
The unmarked angle in the quadrilateral forms a linear pair with angle x.
⇒ unmarked angle + x = 180
⇒ 130 + x = 180
⇒ x = 50°