FIND MISSING ANGLES IN TRIANGLES AND QUADRILATERALS

In this section, you will learn how to find missing angles in triangles and quadrilaterals. 

Practice Problems

Problem 1 :

Find the missing angle in the triangle shown below. 

Solution :

In any triangle, the sum of interior angles is 180°.

In the triangle above, angle B is right angle. That is 90°.

Then, 

∠A + ∠B + ∠C  =  180°

Substitute.

40° + 90° + ∠C  =  180°

130° + ∠C  =  180°

∠C  =  180° - 130°

∠C  =  50°

So, the missing angle is 50°.

Problem 2 :

Find the missing angle in the quadrilateral shown below.

Solution :

In any quadrilateral, the sum of interior angles is 360°.

Then, 

∠A + ∠B + ∠C + ∠D  =  360°

Substitute.

85° + 95° + 120° + ∠D  =  360°

300° + ∠D  =  360°

Subtract 300° from each side. 

∠D  =  60°

So, the missing angle is 60°.

Problem 3 :

Find the missing angle in the square shown below. 

Solution :

In any quadrilateral, the sum of interior angles is 360°.

Then, 

∠D + ∠E + ∠F + ∠G  =  360°

Substitute.

87° + 110° + 65° + ∠G  =  360°

262° + ∠G  =  360°

Subtract 262° from each side. 

∠G  =  98°

So, the missing angle is 98°.

Problem 4 :

Find the value of x in the square shown below. 

Solution :

In a square all angles are right angles.

 ∠S   =  16 x - 6  =  90°

16x - 6  =  90°

16x  =  90° + 6

16x  =  96°

Divide by 16 on both sides

16x/16  =  96/16

x  =  6° 

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