Match the statements with their values. *see photo for reference*

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°

================================================

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°

===================================================

Part (3):

When m∠QRP = 30°, and ΔPQR is an isosceles triangle with PQ = QR

So, m∠QPR = m∠QRP = 30°

====================================================

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°