Question

If two complementary angles differ by 24 degree, find their measures

Answer 1

X+Y=90 DEGREES.
X=Y+24
(Y+24)+Y=90
2Y=90-24
2Y=66
Y=66/2
Y=33 DEGREES FOR THE SMALLER ANGLE
X=33+24=57 DEGREES FOR THE LARGER ANGLE.
PROOF:
33+57=90
90=90

Answer 2

Answer: 57° and 33°

Step-by-step explanation:

• We know sum of complementary angles is 90°.
• Let the angles be x and y.
• So,x+y=90°  and given x-y=24°.
• Adding both the equations we get 2x=114°

                                                               ⇒ x=$\frac{114}{2}$

                                                              ∴ x=57°

• Putting the value of x in above equation

         x+y=90°

     ⇒y=90°-57°

     ∴ y=33°

• Hence,the required angles are 57° and 33°.

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