Question

In each diagram BD bisects ABD find ABC

Answer 1

if BD is bisecting the angle, that simple means the two halves from the bisection are just twins, thus

`\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`

Answer 2

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°