Question

Three angles of a quadrilateral are 35, 65 and 128 degrees. Find the measure of the fourth angle?​

Answer 1

Answer:

The measure of the fourth angle is 1 point 65 75 85 135. 2. See answers. Log in to add ... let 4th angle = a. the sum of the angles of quadrilateral = 360.

Answer 2

$\large{ \sf \underline{Given - }}$

$\sf \dashrightarrow \: Let \: us \: take \: a \: quadrilateral \: ABCD$

$\sf Now , \: by \: the \: given \: information ,$

$\sf \implies \angle{A} = 35 ^{\circ}$

$\sf \implies \angle{B} = 65 ^{\circ}$

$\sf \implies \angle{C} = 128 ^{\circ}$

$\large{ \sf \underline{To \: find - }}$

$\sf \dashrightarrow \: Measure \: of \: the \: fourth \: angle = \: ?$

$\large{ \sf \underline{Solution - }}$

$\sf \dashrightarrow \: \boxed{{\sf{Sum \ of \ all \ angles \ of \ Quadrilateral = 360 ^{\circ}}}}$

$\bf Now,$

$\sf \dashrightarrow \: \sf{\sf \angle A + \angle B + \angle C + \angle D = 360 ^{\circ}}$

$\sf \dashrightarrow \: \sf{\sf 35 ^{\circ} + 65^{\circ} + 128 ^{\circ} + \angle D = 360 ^{\circ}}$

$\sf \dashrightarrow \: \sf{\sf 228 ^{\circ} + \angle D = 360 ^{\circ}}$

$\sf \dashrightarrow \: \sf{\sf \angle D = 360 ^{\circ} - 228 ^{\circ} }$

$\sf \dashrightarrow \: \sf{\sf \angle D = 132 ^{\circ} }$

$\bf Hence,$

$\sf \dashrightarrow \: \underline{\boxed{ \sf Measure \: of \: the \: fourth \: angle = \: 132 ^{\circ}}} \: \bigstar$

$\quad$

$\large{ \sf \underline{Verification - }}$

$\sf\dashrightarrow \: {\sf 35 ^{\circ} + 65 ^{\circ} + 128 ^{\circ} + \angle D = 360 ^{\circ}}$

$\sf\dashrightarrow \: {\sf 35 ^{\circ} + 65 ^{\circ} + 128 ^{\circ} + 132 \degree = 360 ^{\circ}}$

$\sf\dashrightarrow \: {\sf 360 ^{\circ} = 360 ^{\circ}}$

$\sf\dashrightarrow \: {\sf LHS = RHS }$

$\sf\dashrightarrow \: Hence \: verified \: !!$

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$\large{ \sf \underline{More \: information - }}$

$\sf\dashrightarrow \: Sum \: of \: all \: interior \: angles \: of \: a \: quadrateral = 360^{\circ}$

$\sf\dashrightarrow \: Sum \: of \: all \: interior \: angles \: of \: a \: triangle = 180^{\circ}$

$\sf\dashrightarrow \: Sum \: of \: all \: interior \: angles \: of \: a \: Hexagon = 720^{\circ}$

$\sf\dashrightarrow \: Sum \: of \: all \: interior \:angles\:of \:a\: Pentagon = 540^{\circ}$