Question

In Triangle ABC, AC is extended through C to D. If

mZBAC = 6x + 10, m ABC = 6x - 10, and mZBCD= 8x + 20
find x.

Answer 1

X = 5 unit

Explanation:

Given as , ABC is a Triangle ,

AC extended to through C to D

∠BAC = 6x + 10

∠ABC = 6x - 10

∠BCD = ∠ 8x + 20

When c extended to D then , ∠BCD is an external angle

∵ External angle = Sum of opposite internal angles

Or ,∠BCD = ∠BAC + ∠ABC

Or, ∠ 8x + 20 = 6x + 10 + 6x - 10

Or, ∠ 8x + 20 = 12x

Or, 12x - 8x = 20

∴ 4x = 20

So, x =
`(20)/(4)` = 5

Hence the value of X = 5 unit Answer