Question

I need help on this can someone help me thank you it’s geometry:)

Answer 1

Answer: C. 10

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How to get this answer:

The largest angle ABD is 90 degrees because of the small little angle square marker. Another clue is the notation
`BA \perp BD`. The upside down T symbol means "perpendicular", showing the lines BA and BD form a 90 degree angle. The pieces of the angle (ABC = 4x and CBD = 5x) must add up to 90 degrees, or else they wouldn't fit like a jigsaw puzzle.

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(angle ABC) + (angle CBD) = angle ABD

4x + 5x = 90

9x = 90 ... combining like terms

9x/9 = 90/9 ... dividing both sides by 9

x = 10

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If x = 10, then 4x = 4*10 = 40, which is the measure of angle ABC

If x = 10, then 5x = 5*10 = 50 is the measure of angle CBD

We see that ABC+CBD = 40+50 = 90