Question

Need help on the stretch problem.

Answer 1

Step-by-step explanation:

ΔACX is an isosceles triangle, so ∠AXC = ∠XAC.  We'll call the measure of this angle x°.

∠AXC and ∠BXC are supplementary, so ∠AXC + ∠BXC = 180.  That means ∠BXC = 180 − x.

ΔBXC is an isosceles triangle, so ∠XBC = ∠XCB.  We'll call the measure of this angle y°.

Angles of a triangle add up to 180, so:

y + y + (180 − x) = 180

2y = x

y = x/2

∠ACX and ∠XCB are complementary, so ∠ACX + ∠XCB = 90.

x + y = 90

x + x/2 = 90

3/2 x = 90

x = 60

Therefore, ∠AXC = ∠XAC = 60°.