Angles A and B are complementary. Two separate angles are shown. Angle A is (x + 22) degrees. Angle B is x degrees. What is the value of x ?
Angles A and B are complementary.
Two separate angles are shown. Angle A is (x + 22) degrees. Angle B is x degrees.
What is the value of x ?
Answer:
[tex]\mathrm{x=34^o}[/tex]
Step-by-step explanation:
[tex]\mathrm{Since\ A\ and\ B\ are\ complementary\ angles,}\\\mathrm{\angle A+\angle B=90^o}\\\mathrm{or,\ (x+22)^o+x^o=90^o}\\\mathrm{or,\ 2x+22^o=90^o}\\\mathrm{or,\ 2x=68^o}\\\mathrm{or,\ x=34^o}[/tex]
The value of x is :
↬ 34
Solution:
If two angles are complementary, their sum is 90°.
Since A and B are complementary, we know that :
[tex]\rm{A+B=90}[/tex]
The values are x + 22 and x, respectively.
[tex]\rm{x+22+x=90}[/tex]
Combine like terms.
[tex]\rm{2x+22=90}[/tex]
[tex]\rm{2x=68}[/tex]
Divide each side by 2.
[tex]\rm{x=34}[/tex]
The value of the other angle is:
[tex]\rm{x=34+22}[/tex]
[tex]\rm{x=56}[/tex]
Hence, the angles are 34 and 56.
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