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The larger of two supplementary angles is 22° more than the smaller. The smaller angle (in degree) is:
79
84
86
88
79
Subtract the difference from the total sum (180−22=158) and divide by 2 to get the smaller angle (158/2=79).
Two angles are supplementary, meaning their sum is 180°. The larger angle is 22° more than the smaller angle.
x+(x+22)=180
Subtract the difference from the total sum (180−22=158) and divide by 2 to get the smaller angle (158/2=79).
Students often solve for the larger angle by mistake or use 90° (complementary) instead of 180° (supplementary).
Define variables
Let the smaller angle be x. Since the larger is 22° more, the larger angle is x+22.
x,x+22
Set up the equation
Supplementary angles sum to 180°. So, add the two expressions and equate to 180.
x+(x+22)=180
Solve for x
Combine like terms to get 2x+22=180. Subtract 22 from both sides (180−22=158) and divide by 2.
2x=158⟹x=79
A is correct because the calculation (180−22)/2=79 gives the smaller angle.
This concept of finding values from a known sum and difference is identical to solving 'Age' problems in Quantitative Aptitude.
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