Question #c679c

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Question #c679c

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Answer 1 · 2016-10-07T20:19:12

$x = 7$ $x = 7$

Explanation:

As $¯ ¯¯¯¯ ¯ B D$ $bar(BD)$ bisects $∠ A B C$ $angleABC$ , we have

$m ∠ A B D = \frac{1}{2} m ∠ A B C = \frac{1}{2} (40^{\circ}) = 20^{\circ}$ $mangleABD = 1/2mangleABC = 1/2(40^@) = 20^@$

Equating that with one of the given equations for $x$ $x$ , we have

$3 x - 1 = 20$ $3x-1 = 20$

$\Rightarrow 3 x = 21$ $=> 3x = 21$

$:. x = 7$

As a side note, we could also have arrived at the same conclusion by noting that $mangleABD = mangleCBD$ and setting $3x-1 = 34-2x$ , then solving for $x$ .

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Question #c679c

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