Answer:
y = 10
z = 31°
Step-by-step explanation:
Properties of an isosceles triangle
- Two sides equal in length (legs).
- Vertex: The angle between the two legs.
- Base: The side opposite the vertex. Base angles are equal.
- The line segment that bisects the vertex is perpendicular to the base and bisects the base.
The dashes on the line segments of the triangle indicate that the line segments are equal in length, so EF = EH.
Therefore, the triangle is an isosceles triangle with base HF.
The line segment EG bisects the vertex E of the triangle. Therefore, EG is the perpendicular bisector of HF. This means that HG = GF, and ΔFGE and ΔHGE are congruent right triangles.
Therefore:
HG = GF = 10 ⇒ y = 10
Interior angles of a triangle sum to 180°.
⇒ ∠FGE + ∠GEF + ∠EFG = 180°
⇒ 90° + z + 59° = 180°
⇒ z = 180° - 59° - 90°
⇒ z = 31°
