3 Marks Question

Question 13 Marks

A quadrilateral has three acute angles, each measuring $75^\circ $. Find the measure of the fourth angle.

Answer

Three acute angles of a quadrilateral are $75^\circ $ each
, Sum of three angles $= 3 \times 75^\circ = 225^\circ $ But
sum of $4$ angles$ = 360^\circ $
Fourth angle $= 360^\circ - 225^\circ = 135^\circ .$

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Question 23 Marks

The three angles of a quadrilateral are $76^\circ , 54^\circ$ and $108^\circ $. Find the measure of the fourth angle.

Answer

We know that, Sum of $4$ angles of a duadrilateral $= 360^\circ $ But
sum of $ 3$ angles$ = 76^\circ + 54^\circ + 108^\circ = 238^\circ $
$4$th angle $= 360 - 238^\circ = 122^\circ $
Hence, measure of fourth angle $= 122^\circ .$

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Question 33 Marks

Two angles of a quadrilateral measure $85^\circ $ and $75^\circ $ respectively. The other two angles are equal. Find the measure of each of these equal angles.

Answer

Sum of $4$ angles of a quadrilateral $360^\circ $,
Sum of two angles $= 85^\circ + 75^\circ = 160^\circ $
Sum of other two angles $= 360^\circ - 160^\circ = 200^\circ $ But each of these two angles are equal
, Measure of each equal angle $=\frac{200^\circ}{2}$ $= 100^\circ $

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Question 43 Marks

The angles of a quadrilateral are in the ratio $3 : 5 : 7 : 9.$ Find the measure of each of these angles.

Answer

Ratio of four angles of a quadrilateral $= 3 : 5 : 7 : 9$
Let these angles be $3x, 5x, 7x$ and $9x$ Then $3x + 5x + 7x + 9x = 360^\circ $ (sum of angles)
$\Rightarrow 24x = 360º$
Frist angle $= 3x 3 \times 15^\circ = 45^\circ $
Second angle $= 5x = 5 \times 15^\circ = 75^\circ $
Third angle $= 7x = 7 \times 15^\circ = 105^\circ $ Fourth angle $= 9x = 9 \times 15^\circ = 135^\circ$

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Question 53 Marks

Three angles of a quadrilateral are equal and the measure of the fourth angle is $120^\circ $. Find the measure of each of the equal angles.

Answer

Sum of $4$ angles of a quadrilateral $360^\circ $, One angles $= 120^\circ $
Sum of other three angles $= 360^\circ - 120^\circ = 240^\circ $
But each of these $3$ angles are equal, Each of eqaul angle $=\frac{240^\circ}{3}$ $= 80^\circ $

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