Question

Two angles of a quadrilateral are complementary angles and the remaining two angles are differ by 12 degree. Find the largest angle of the quadrilateral.

Answer 1

The largest angle in the quadrilateral is 141°.

• Let the angles of the quadrilateral be a,b,c,d.
• Two angles of a quadrilateral are complementary angles.

a+b=90   ....(Equation 1)

• Remaining two angles of the quadrilateral differ by 12.

c-d = 12    .....(Equation 2)

• Now sum of all angles of the quadrilateral is 360°.

a+b+c+d =360°    .....(Equation 3)

• Substituting the value of (a+b) in equation 3

c + d =360 - 90

c + d = 270    ....(Equation 4)

• Solving equation 2 and 4, we get

2c = 282

c = 141°

• Now substituting value of c in equation 2

d = 141 - 12

d = 129°

• a and b are complementary angles therefore they cannot be greater than 90°. Therefore the largest angle is c = 141°.

Answer 2

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The largest angle in the quadrilateral is 141°.

Let the angles of the quadrilateral be a,b,c,d.

Two angles of a quadrilateral are complementary angles.

a+b=90   ....(Equation 1)

Remaining two angles of the quadrilateral differ by 12.

c-d = 12    .....(Equation 2)

Now sum of all angles of the quadrilateral is 360°.

a+b+c+d =360°    .....(Equation 3)

Substituting the value of (a+b) in equation 3

c + d =360 - 90

c + d = 270    ....(Equation 4)

Solving equation 2 and 4, we get

2c = 282

c = 141°

Now substituting value of c in equation 2

d = 141 - 12

d = 129°

a and b are complementary angles therefore they cannot be greater than 90°. Therefore the largest angle is c = 141°.