Answer:
16) ∠ABC = 48°
17) ∠ABC = 98°
Step-by-step explanation:
Bisect: To divide into two equal parts.
Question 16
First find the value of x.
If BD bisects ∠ABC then:
⇒ ∠ABD = ∠DBC
⇒ 4x = 3x + 6
⇒ 4x - 3x = 3x + 6 - 3x
⇒ x = 6
Substitute the found value of x into the equation of ∠ABC:
⇒ ∠ABC = ∠ABD + ∠DBC
⇒ ∠ABC = 4x + 3x + 6
⇒ ∠ABC = 4(6) + 3(6) + 6
⇒ ∠ABC = 24 + 18 + 6
⇒ ∠ABC = 42 + 6
⇒ ∠ABC = 48°
Question 17
First find the value of x.
If BD bisects ∠ABC then:
⇒ ∠ABD = ∠DBC
⇒ 5x - 11 = 4x + 1
⇒ 5x - 11 - 4x = 4x + 1 - 4x
⇒ x - 11 = 1
⇒ x - 11 + 11 = 1 + 11
⇒ x = 12
Substitute the found value of x into the equation of ∠ABC:
⇒ ∠ABC = ∠ABD + ∠DBC
⇒ ∠ABC = 5x - 11 + 4x + 1
⇒ ∠ABC = 9x - 10
⇒ ∠ABC = 9(12) - 10
⇒ ∠ABC = 108 - 10
⇒ ∠ABC = 98°
