Question

If DB bisects ADC m<1=(3x+4), and m<2=(5x-2) find x

Answer 1

Answer on Question #57012 – Math – Geometry

If DB bisects ADC m<1=(3x+4), and m<2=(5x-2) find x

Solution

If angles $\angle 1$ and $\angle 2$ are corresponding, or alternate interior, or alternate exterior, then they are equal, hence their measures are equal

$$\Rightarrow 3x + 4 = 5x - 2 \Rightarrow 2x = 6 \Rightarrow x = 3.$$

If angles $\angle 1$ and $\angle 2$ are consecutive interior angles, then they add up to $180{}^{\circ}$, hence

$$3x + 4 + 5x - 2 = 180$$ $$8x + 2 = 180$$ $$8x = 178$$ $$x = \frac{178}{8},$$

that is,

$$x = 22{}^{\circ} 15'.$$

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