Q. 154.6( 21 Votes )
The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
Answer :
Given: The larger of two supplementary angles exceeds the smaller by 18 degrees.
To find: The measure of both angles.
solution:
Let the larger angle be ‘a’ and the smaller angle be ‘b’.
Given, larger of two supplementary angles exceeds the smaller by 18 degrees.
⇒ a = b + 18
⇒ a - b = 18 ...... (1)
The sum of supplementary angles is 180°.
⇒a + b = 180.....(2)
Adding the equations 1 and 2 we get,
⇒ 2a = 198
⇒ a = 99°
Put the value of b in eq. 1 to get,
99-b=18
⇒ -b=18-99
⇒ -b=-81
⇒ b=81
Thus, b = 81°
Hence the measure of smaller angle is 81° and larger angle is 99°.
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