Question 1204771: In the triangle shown here: https://ibb.co/Ch9FTZT, DB = DC , DE = CE and
∠DAE = 42°. Find the measure of ∠ACB.
I understand Mr.Greenstamps posted a solution, but it was a "Here's a hint, now you solve it!" But my IQ is far too low to solve it despite all the information he gave. Please help.
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
DB = DC which makes triangle BDC isosceles.
It will mean base angles B and C are congruent.
In other words, angle DBC = angle DCB.
Let x represent the measure of each base angle.
The congruent base angles are opposite the congruent sides.
Because BC is parallel to DE (due to the arrow markers), we know that alternate interior angles BCD and EDC are congruent.
Both are x.
Triangle DEC is isosceles since DE = CE.
The congruent base angles are D and C (aka angle EDC and angle ECD).
Each of these angles are x.
Focus on triangle DEC. Use the remote interior angle theorem to find that (angleEDC)+(angleECD) = angleAED
Or you can use the corresponding angles theorem to see that angle ACB = angle AED.
This will lead to angle AED = 2x
Use the corresponding angles theorem to note that angle ADE = angle ABC = x.
Here's a diagram summarizing all that we found so far
From here focus on triangle AED.
For any triangle, the interior angles always add to 180 degrees.
A+E+D = 180
42+2x+x = 180
I'll let you take over from here.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
(1) DB = DC, so angles DBC and DCB are congruent. Let x be the measure of each.
(2) In triangle DBC, that makes the measure of angle BDC 180-2x.
(3) DE is parallel to BC, so the measure of angle ADE is also x.
(4) Angles ADE, DEC, and CDB together make a straight angle which has a measure of 180; that with (2) makes x the measure of angle EDC.
(5) Since DE = CE, the measure of angle DCE is also x.
(6) Angle ACB now has measure x+x = 2x.
(7) Again since DE and BC are parallel, angle DEA has measure 2x.
(8) In triangle ADE, the measures of the three angles are x, 2x, and 42. Since their sum is 180...
x+2x+42=180
3x+42=180
3x=138
x=46
ANSWER: The measure of angle ACB is 2x = 92 degrees
|
|
|
