Answer:
Your answer is ∠BDC = 70°
Step-by-step 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:
[tex] \therefore m\angle BDC = 70\degree[/tex]
Step-by-step explanation:
[tex] m\angle BDC +m\angle CDA = m\angle BDA[/tex]
(Angle sum postulate)
[tex] (-3x + 34)\degree +(-2x + 56)\degree = 150\degree [/tex]
[tex] (-5x + 90)\degree = 150\degree [/tex]
[tex] -5x + 90 = 150 [/tex]
[tex] -5x = 150-90 [/tex]
[tex] -5x = 60[/tex]
[tex] x = \frac{60}{-5}[/tex]
[tex] x = -12[/tex]
[tex] \because m\angle BDC = (-3x + 34)\degree[/tex]
[tex] \therefore m\angle BDC = [-3\times(- 12) + 34)\degree[/tex]
[tex] \therefore m\angle BDC = 70\degree[/tex]
