Foreverisabell
Find the measure of angle DCA if D is the incenter of the triangle ABC.
Explain step by step please!
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Foreverisabell
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Foreverisabell
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@ZeHanz this one.
ZeHanz
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OK, the incenter is the intersection of the angle bisectors.
You have two more angles now!
Foreverisabell
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Also in this one, would y = 60?
Foreverisabell
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Alright,
ZeHanz
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y=60 degrees, if the triangle is supposed to be equilateral.
Foreverisabell
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alright , now for the other problem, how do you find the measure of angle DCA?
ZeHanz
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Better question, what are the measures of the angles CAB and ABC?
Foreverisabell
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111 is the measure of ABC
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I meant they all equal 180. But the missing one is 111.
Foreverisabell
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which is c?
ZeHanz
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DOn't know how you get these numbers.
Remember: the lines drawn to the incenter are the angle bisectors.
That means:
angle CAB = 2*32 = ...
angle ABC = 2*37 = ...
Add these and subtract from 180 to get angle ACB.
Foreverisabell
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yeah I got 42.
ZeHanz
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That's right!
Foreverisabell
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But why did you times 2 times each?
Foreverisabell
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never mind I know why now.
Foreverisabell
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So the measure of angle DCA would be 32 + 42 + what?
ZeHanz
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Look at the drawing. The numbers are the measures of half the angles, because the lines to the incenter are the: angle b i s e c t o r s...
ZeHanz
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DC is bisector of the angle we just found: 42 degrees, so 21 degrees is the measure of DCA!
Foreverisabell
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But I thought the wanted the measure of the whole angle?
Foreverisabell
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Measure of DCA = 21 degrees it seems really small?
ZeHanz
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I'll make a drawing, hold on...
Foreverisabell
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alright
Foreverisabell
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Im pretty sure I understand now. They just want the measure of C?
Foreverisabell
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Also I know that a squared + b squared = c squared. But this triangles does not show any angles so except 90 degrees. So Im not sure how to find x?
Foreverisabell
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@ZeHanz
ZeHanz
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If there is a right angle in the triangle (there is!) then a²+12²=20².
You can work out a now.
Foreverisabell
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Yeah But I can't seem to get it? how to get a?
Foreverisabell
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@ZeHanz
ZeHanz
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a²+144=400, so a²=?
Foreverisabell
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16?
ZeHanz
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a²=256, so a=16, right!
Foreverisabell
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thank you!
ZeHanz
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yw!