3 Mark Question

Question 13 Marks

A quadrilateral has three acute angles, each measuring 75°. Find the measure of the fourth angle.

Answer

Three acute angles of a quadrilateral are 75º each,
Sum of three angles = 3 × 75º = 225º
But sum of 4 angles = 360º
Fourth angle = 360º - 225º
= 135º.

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Question 23 Marks

The three angles of a quadrilateral are 76°, 54° and 108°. Find the measure of the fourth angle.

Answer

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

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Question 33 Marks

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

Answer

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

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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 = 360º (sum of angles)
⇒ 24x = 360º
Frist angle = 3x 3 × 15º = 45º
Second angle = 5x = 5 × 15º = 75º
Third angle = 7x = 7 × 15º = 105º
Fourth angle = 9x = 9 × 15º = 135º

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Question 53 Marks

Three angles of a quadrilateral are equal and the measure of the fourth angle is 120°. Find the measure of each of the equal angles.

Answer

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

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