angle P and angle Q are complementary angles. | vedclass

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Question

(A) Two angles are complementary if their sum is $90^{\circ}$.Therefore,$\angle P + \angle Q = 90^{\circ}$.Substituting the given expressions: $(3x +

Vedclass · Accepted Answer

$\angle P = 66^{\circ}, \angle Q = 24^{\circ}$

Vedclass · Answer

(A) Two angles are complementary if their sum is $90^{\circ}$.Therefore,$\angle P + \angle Q = 90^{\circ}$.Substituting the given expressions: $(3x + 15^{\circ}) + (x + 7^{\circ}) = 90^{\circ}$.Combining like terms: $4x + 22^{\circ} = 90^{\circ}$.Subtracting $22^{\circ}$ from both sides: $4x = 68^{\circ}$.Dividing by $4$: $x = 17^{\circ}$.Now,calculate $\angle P$: $\angle P = 3(17^{\circ}) + 15^{\circ} = 51^{\circ} + 15^{\circ} = 66^{\circ}$.Calculate $\angle Q$: $\angle Q = 17^{\circ} + 7^{\circ} = 24^{\circ}$.Thus,$\angle P = 66^{\circ}$ and $\angle Q = 24^{\circ}$.

$\angle P$ and $\angle Q$ are complementary angles. If $\angle P = 3x + 15^{\circ}$ and $\angle Q = x + 7^{\circ}$,then find $\angle P$ and $\angle Q$.

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