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Given that ABD and BDE are complementary angles with an angle measurement of 3x - 2 for ABD and 5x + 22 for BDE, find the value of x.

(a) 8.75
(b) 10
(c) 7.5
(d) 12

User Kumiau
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1 Answer

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Final answer:

To solve for x, the algebraic expressions representing the angles are summed up and set equal to 90 degrees, resulting in x being 8.75. Hence, the correct answer is option (a) 8.75.

Step-by-step explanation:

The student is asking for help in solving a problem involving complementary angles and algebraic expressions. Given that ABD and BDE are complementary angles, the sum of the angles should equal 90 degrees. We’re told that ABD is 3x - 2 degrees and BDE is 5x + 22 degrees. To find the value of x, we need to set up the equation:

3x - 2 + 5x + 22 = 90

This simplifies to:

8x + 20 = 90,

which further simplifies to:

8x = 70.

Now we divide both sides by 8 to get:

x = 8.75.

Therefore, the correct answer is option (a) 8.75.

User Andromida
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