if BD is bisecting the angle, that simple means the two halves from the bisection are just twins, thus
[tex] \bf \boxed{26}~\hspace{5em} 5x+2=7x-6\implies 8=2x\implies \cfrac{8}{2}=x\implies 4=x \\\\[-0.35em] ~\dotfill\\\\ \boxed{27}~\hspace{5em} 11x-12=8x+3\implies 3x=15\implies x=\cfrac{15}{3}\implies x=5 \\\\[-0.35em] ~\dotfill\\\\ \boxed{28}~\hspace{5em} 5x+13=9x-23\implies 36=4x\implies \cfrac{36}{4}=x\implies 9=x [/tex]
Answer:
Given, line BD bisects ∠ABD.
This means Line BD divides the ∠ABD into two equal parts.
⇒ ∠ABD = ∠DBC
and ∠ABC = ∠ABD + ∠DBC
⇒ ∠ABC = 2 × ∠ABD
Then,
26. 5x + 2 = 7x - 6
⇒ 2x = 8
⇒ x = 4
⇒ ∠ABC = 2 × (5 × 4 + 2) = 44°
27. 11x - 12 = 8x + 3
⇒ 3x = 15
⇒ x = 5
⇒ ∠ABC = 2 × (11 × 5 - 12) = 86°
28. 5x + 13 = 9x - 23
⇒ 4x = 36
⇒ x = 9
⇒ ∠ABC = 2 × (5 × 9 +13) = 116°
