angle ABD and angle DBC are adjacent angles. | vedclass

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Question

(A) Since $\angle ABD$ and $\angle DBC$ are adjacent angles,their sum is equal to $\angle ABC$.Therefore,$\angle ABD + \angle DBC = \angle ABC$.Substi

Vedclass · Accepted Answer

$x = 20^{\circ}, \angle ABD = 30^{\circ}, \angle DBC = 40^{\circ}$

Vedclass · Answer

(A) Since $\angle ABD$ and $\angle DBC$ are adjacent angles,their sum is equal to $\angle ABC$.Therefore,$\angle ABD + \angle DBC = \angle ABC$.Substituting the given values: $1.5x + 2x = 70$.$3.5x = 70$.$x = \frac{70}{3.5} = 20$.Now,calculate the angles:$\angle ABD = 1.5 	imes 20^{\circ} = 30^{\circ}$.$\angle DBC = 2 	imes 20^{\circ} = 40^{\circ}$.Thus,$x = 20$,$\angle ABD = 30^{\circ}$,and $\angle DBC = 40^{\circ}$.

$\angle ABD$ and $\angle DBC$ are adjacent angles. If $\angle ABD = 1.5x^{\circ}$,$\angle DBC = 2x^{\circ}$,and $\angle ABC = 70^{\circ}$,then find $x$ and the measures of $\angle ABD$ and $\angle DBC$.

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