Question

In the diagram, mZBDA = 150°. Find mZBDC.

Answer 1

Your answer is ∠BDC = 70°

Explanation:

So you know that the total angle is 150°. Given that, we can set the two equations equal to 150° because we know that they add to 150°.

-3x + 34 + -2x + 56 = 150

First, combine the like terms.

-3x - 2x = -5x

34 + 56 = 90

-5x + 90 = 150

Get the -5x by itself by subtracting 90 from 150.

150 - 90 = 60

Now you have:

-5x = 60

Get the x alone by dividing both sides by -5.

-5x/-5 = 1x (written as just x, though)

60/-5 = -12

Therefore, x = -12.

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Given that x = -12, We can substitute -12 in place of "x" into the equation desired to solve, in this case that angle we want to solve for is ∠BDC.

∠BDC is represented by the equation (-3x + 34)

Substitute -12 in place of x and solve.

-3(-12) +34

36 + 34

= 70

Therefore ∠BDC = 70°.

Answer 2

`\therefore m\angle BDC = 70\degree`

Explanation:

`m\angle BDC +m\angle CDA = m\angle BDA`

(Angle sum postulate)

`(-3x + 34)\degree +(-2x + 56)\degree = 150\degree`

`(-5x + 90)\degree = 150\degree`

`-5x + 90 = 150`

`-5x = 150-90`

`-5x = 60`

`x = (60)/(-5)`

`x = -12`

`\because m\angle BDC = (-3x + 34)\degree`

`\therefore m\angle BDC = [-3*(- 12) + 34)\degree`

`\therefore m\angle BDC = 70\degree`