Answer:
See the attached figure.
Step by step solution:
Part (1):
When ΔABC is an isosceles triangle with AB = AC
The summing of the three of the triangle = 180°
∴ m∠ABC + m∠BAC + m∠ACB = 180°
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Part (2):
When ΔABC is an isosceles triangle with AB = AC
So, m∠ABC = m∠ACB = x
if m∠BAC = 70
∵ m∠ABC + m∠ACB + m∠BAC= 180°
∴ x + x + 70 = 180 ⇒ x = 55°
∴ m∠ABC = 55°
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Part (3):
When m∠QRP = 30°, and ΔPQR is an isosceles triangle with PQ = QR
So, m∠QPR = m∠QRP = 30°
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Part (4):
When m∠BAC = 45° and points D and E are the midpoints of AB and BC in ΔABC
∵ Points D and E are the midpoints of AB and BC in ΔABC
∴ DE // AC
∴ m∠BDE = m∠BAC ⇒ the corresponding angles are congruent
∴ m∠BDE = 45°
