The definition of an angle bisector is a bisector that cuts an angle into two equal halves.
So BD bisects ∠ABC, therefore ∠ABD = ∠DBC
We can set the expressions inside them equal to each other, solve for x, and substitute it into the expressions again to find the total value of the angle.
4x - 15 = 3x + 12
- 3x - 3x
______________
x - 15 = 12
+ 15 + 15
______________
x = 27
So x = 27, we can plug this back into an expression and do the same with the second one and add them, or, because we know they are equal, just multiply two once we find the value of the first one.
4(27) - 15
= 108 - 15
= 93
Multiply 93 by 2.
93 x 2 = 186
Therefore m∠ABC is 186°
Hope this helps! :)
<span>Read the problem.Begin by reading the problem carefully. Don’t jump to any conclusions about the answer until you understand the problem.<span>Identify and list the facts.Look at all the information given in the story problem and make a list of what you know.</span><span>Figure out exactly what the problem is asking for.Know what you’re trying to find. The problem often states the required answer, but sometimes you have to ferret it out from the information given. If an important fact isn’t there, you can often convert some piece of the given information.</span><span>Eliminate excess information.The problem may include facts that don’t help you find the solution, so clear them out of the way.</span><span>Pay attention to units of measurement.For example, if dimensions are given in inches, but the answer must be in square feet, you need to convert units. You can use a table of conversions, an online calculator, or your own memory to get the conversion factors.</span><span>Draw a diagram.Sometimes a diagram helps you visualize the problem (but not always).</span><span>Find or develop a formula.When you see the math that needs to be done, you probably know a common math formula to use for the computation. You will find that you use some special formulas again and again.</span><span>Consult a reference.If you’re stuck, look for a reference of some kind, such as a conversion chart or even a blog where someone has encountered the same problem you’re having (although as always, consider Internet sources carefully).</span><span>Do the math and check your answer.After you have an answer, be sure to test it. If the result is outrageously high or low, verify whether you made a mistake.</span></span>
