angle P and angle Q are supplementary angles. | vedclass

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Question

(A) Two angles are supplementary if their sum is $180^{\circ}$.Given: $\angle P + \angle Q = 180^{\circ}$ (Equation $1$)Given: $\angle P = \angle Q +

Vedclass · Accepted Answer

$\angle P = 107.5^{\circ}, \angle Q = 72.5^{\circ}$

Vedclass · Answer

(A) Two angles are supplementary if their sum is $180^{\circ}$.Given: $\angle P + \angle Q = 180^{\circ}$ (Equation $1$)Given: $\angle P = \angle Q + 35^{\circ}$ (Equation $2$)Substitute Equation $2$ into Equation $1$:$(\angle Q + 35^{\circ}) + \angle Q = 180^{\circ}$$2\angle Q + 35^{\circ} = 180^{\circ}$$2\angle Q = 180^{\circ} - 35^{\circ}$$2\angle Q = 145^{\circ}$$\angle Q = 145^{\circ} / 2 = 72.5^{\circ}$Now,find $\angle P$ using Equation $2$:$\angle P = 72.5^{\circ} + 35^{\circ} = 107.5^{\circ}$Thus,$\angle P = 107.5^{\circ}$ and $\angle Q = 72.5^{\circ}$.

$\angle P$ and $\angle Q$ are supplementary angles. If $\angle P = \angle Q + 35^{\circ}$,then find $\angle P$ and $\angle Q$.

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