find the size of the each letterd angle stating the reasons for each Step.please help out .this is Edexcel INTERNATIONAL GCSE(9-1) for grade 7 ....... please help me out to solve this sum
Answers
Answer:
see below
Step-by-step explanation:
theorem 1 : angles opposite to equal sides in a triangle are equal
theorem 2 : A diameter in a circle makes 90°on the circumference
theorem 3 : A tangent makes 90° with the radius
(1) two sides (radii) are equal...hence
a = 50°
a + 50° + ? = 180° ( ang-sum prp)
? = 180 - 50 - 50 = 80°
b = 360° - 80° ( rflx ang)
b = 280°
(2) a = 90° ( theorem 2)
b = 180 - 90 - 60° ( ang sum prp)
b = 30°
(3) ? = a ( theorem 1)
a + ? + 40 = 180 ( ang sum prp)
2a = 180 - 40
a = 70°
since...the larger triangle is a Right triangle ( theorem 2)
the remaining Angles add up to 90°
a + b = 90°
b = 90 - 70
b = 20°
(4) ? + 35 = 90 ( theorem 2)
? = 90 - 35
? = 55°
now ..
a = 55° ( theorem 1)
a + 55 + b = 180 ( ang sum prp)
55 + 55 + b = 180
b = 180 - 110
b = 70°
(5) a = b ( theorem 1)
a + b + 130 = 180 ( ang sum prp)
a + a + 130 = 180
2a = 180 - 130
a = 25°; b = 25°
a + c = 90° ( theorem 2)
c = 90 - 25
c = 65°
(6) x + 2x = 90° ( theroem 2)
3x = 90
x = 30°
(7) a = 90° ( theorem 3)
b + 60 = 90 ( theorem 3)
b = 90 - 60
b = 30°
b + c = 90 ( theorem 2)
30 + c = 90
c = 90 - 30
c = 60°