Answer:

first apply exterior angle property then find the other variable finnaly u can find the c variable

The value of

• angle a = 55°
• angle b = 53°
• angle c = 72°

Step by step explanation

• Look at the attached image.

Name the sides

• extend BA to M
• extend RC to N

So,

Given

AB || CR, similarly BM || NR

Here AC is transversal.

➝ ∠BAC = ∠ACR = 72° = ∠c

• alternate interior angles

Now

∠QCR + ∠RCA + ∠ACB = 180°

• (supplementary angles)

➜ 55° + 72° + ∠ACB = 180°

➜ 127° + ∠ACB = 180°

➜ ∠ACB = 180° - 127°

➜ ∠ACB = 53° = ∠b

Also,

∆ABC sum of three angles is 180°

∠BAC + ∠ACB + ∠ABC = 180°

☞ 72° + 53° + ∠ABC = 180°

☞ 125° + ∠ABC = 180°

☞ ∠ABC = 180° - 125°

☞ ∠ABC = 55° = ∠a

Hence

∠a = 55°

∠a = 55°∠b = 53°

∠a = 55°∠b = 53°∠c = 72°