2. BT bisects ZABC. MZABT = 4x-16 and m CBT = 2x + 6 Find MZABT.

The measure of angle ABT is 28°

Step-by-step explanation:

* Lets revise the bisector of a angle

- If a ray bisects and angle that mean the ray divide the angle into

two equal parts in measure

- Ex: if the ray BD bisects angle ABC, then the measure of angle ABD is

equal to the measure of angle CBD

* Lets solve the problem

∵ BT bisects ∠ABC

∴ m∠ABT = m∠CBT

∵ m∠ABT = 4x - 16

∵ m∠CBT = 2x + 6

- Equate the two values

∴ 4x - 16 = 2x + 6

- Lets solve the equation by subtracting 2x from both sides and

adding 16 to both sides

∴ 4x - 2x = 6 + 16

∴ 2x = 22 ⇒ divide both sides by 2

∴ x = 11

- Lets find the measure of angle ABT

∵ m∠ABT = 4x - 16

- Substitute x by 11

∴ m∠ABT = 4 (11) - 16 = 44 - 16 = 28°

* The measure of angle ABT is 28°