Answer:
The measure of ∠CAD is 69°
Step-by-step explanation:
In ΔABC
∵ D is the mid-point of AB
∵ E is the mid-point of BC
∴ DE is parallel to AC
→ From parallelism
∵ DE // AC
∴ m∠EDB = m∠CAD → corresponding angles
∵ m∠EDB = 83 - 7x
∵ m∠CAD = 7x + 55
→ Equate them
∴ 7x + 55 = 83 - 7x
→ Add 7x to both sides
∵ 7x + 7x + 55 = 83 - 7x + 7x
∴ 14x + 55 = 83
→ Subtract 55 from both sides
∵ 14x + 55 - 55 = 83 - 55
∴ 14x = 28
→ Divide both sides by 14
∴ x = 2
→ To find m∠CAD, substitute x by 2 in its measure
∵ m∠CAD = 7(2) + 55
∴ m∠CAD = 14 + 55
∴ m∠CAD = 69°
∴ The measure of ∠CAD is 69°
