Answer:
1. x = 47°
2. c = 47°
Step-by-step explanation:
Question 1
Triangle DEF is an isosceles triangle since it has two sides of equal length.
The two equal sides are called the legs and the angle between them is called the vertex angle. Therefore, the vertex angle of ΔDEF is ∠D.
The side opposite the vertex angle is called the base (EF) and base angles are equal:
⇒ m∠F = m∠E
⇒ x = 47°
Question 2
Triangle STU is an isosceles triangle since it has two sides of equal length.
The two equal sides are called the legs and the angle between them is called the vertex angle. Therefore, the vertex angle of STU is ∠T.
The side opposite the vertex angle is called the base (SU) and base angles are equal.
As the interior angles of a triangle sum to 180° and the base angles are equal:
⇒ m∠S + m∠T + m∠U = 180°
⇒ c + 86° + c = 180°
⇒ 2c = 94°
⇒ c = 47°
