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irina [24]
3 years ago
5

AB is the bisector of CAD. If the mCAB = 2x+30 and m DAB=5x+12 what is the mCAB

Mathematics
1 answer:
Dima020 [189]3 years ago
3 0

Answer:

CAB = 42

Step-by-step explanation:

Given

CAB = 2x + 30

DAB = 5x + 12

Bisector: AB

Required

Find CAB

Since AB bisects CAD, then

CAB = DAB

This is so because AB divides CAD into two equal parts which are CAB and DAB

CAB = DAB

Substitute values for CAB and DAB

2x + 30 = 5x + 12

Collect Like Terms

2x- 5x = 12 - 30

-3x = -18

Divide both sides by -3

x = 6

To solve for CAB, we simply substitute 6 for x in CAB = 2x + 30

CAB = 2 * 6 + 30

CAB = 12 + 30

CAB = 42

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By using the point-slope form of the equation of a line, by knowing the gradient of that line and a point on that line, the equation of this line can be derived.

Now, the point-slope form exists as y - y₁ = m ( x - x₁)

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