Answer:
= 0.6 inch
m∠ABC = 60°
Explanation:
The given parameters are;
The given triangle ΔABC = A right triangle
The angle bisector of ∠CBA = BL
The length of BL = LB = 1.2 in.
The length of LC = 0.6 in.
We have;
≅
reflexive property
∠ABC = ∠CBL + ∠DBL and ∠CBL ≅ ∠DBL definition of bisected angle
∠CBL = ∠DBL by definition of congruency
∠CLB + ∠CBL = ∠CLB + ∠DBL = 90°, opposite angles of a the right angle triangle are supplementary
∴ ∠CLB = ∠CLB by addition property of equality
ΔLDB ≅ ΔLBC are congruent by the Angle-Side-Angle rule of congruency
∴
≅
Congruent Parts of Congruent Triangles are Congruent (CPCTC)
=
= 0.6 in. by definition of congruency
= 0.6 in.
sin(m∠CBL) = Opposite side/(Hypotenuse side) =
/
= 0.6/1.6 = 1/2
m∠CBL = sin⁻¹(1/2) = 30°
m∠CBL = m∠DBL = 30°
m∠ABC = m∠CBL + m∠DBL = 30° + 30° = 60°
m∠ABC = 60°