Question

If CE bisects ZBCD and if m ZBCE = 3x - 6

and mZECD = 2x + 11, find mZBCD. Is
ZBCD acute, right, or obtuse?

Answer 1

m∠BCD = 90°

∠BCD is a right angle

Explanation:

If a ray bisects an angle, that means it divides the angle into two equal parts in measure

∵ Ray CE bisects ∠BCD

→ Means divide it into two angles BCE and ECD which equal in measures

∴ m∠BCE = m∠ECD =
`(1)/(2)` m∠BCD

∵ m∠BCE = 3x - 6

∵ m∠ECD = 2x + 11

→ Equate them to find x

∴ 3x - 6 = 2x + 11

→ Add 6 to both sides

∵ 3x - 6 + 6 = 2x + 11 + 6

∴ 3x = 2x + 17

→ Subtract 2x from both sides

∵ 3x - 2x = 2x - 2x + 17

∴ x = 17

∵ m∠BCE =
`(1)/(2)` m∠BCD

→ Substitute x in the measure of ∠BCE to find it, then use it to

find m∠BCD

∵ m∠BCE = 3(17) - 6 = 51 - 6

∴ m∠BCE = 45°

∵ 45 =
`(1)/(2)` m∠BCD

→ Multiply both sides by 2

∴ 90 = m∠BCD

∴ m∠BCD = 90°

→ The measure of the acute angle is less than 90°, the measure of

the obtuse angle is greater than 90°, and the measure of the

right angle is 90°

∴ ∠BCD is a right angle