Triangle ABC is isosceles with AC = BC and a vertex angle of 50 degrees.
If AD = BE, what is the measure of angle ADE?
State your solution and be sure to explain your reasoning clearly. Explain what steps you took to get your answer. Use complete sentences and grammar. Use the rubric I posted this week to help you determine what grade you will get on your writing.
REMEMBER: Your work is due by Friday Oct. 25th before school is over.
Solution
Angle ACB = 50 degrees. A triangle has a sum of 180 degrees. Subtract 50 from 180 equals 130 degrees left over. Since AC = CB that means two sides of the triangles are the same measure, which in turn means the triangle is an isosceles triangle, that means that the other two vertices must be the same measure. So, divide the remaining degrees by 2. That means angle CDE and angle CED are both 65 degrees.
But we are solving for angle ADE. Angle CDE and angle ADE are lying on a straight line so the sum of the two angles have to equal 180 degrees. If we take 180 and subtract 65 degrees (since we already discovered the measure of CDE was 65 degrees,) that leaves us with 115 degrees. So, angle ADE equals 115 degrees.
Think about...
If ADE is 115 degrees, can you label all of the angles in both triangles?
J.S. P6 I think ADE would be like 130 degrees , what I did is I saved the picture and went to the Desmos Geometry and used that tool, and it helped me.
ReplyDeleteI think the measurement could be deb
ReplyDeleteApc p1: 50??
ReplyDeleteI think the angle ADE is around 135 degrees. This is because the angle seems more than 90 degrees. When I made the angle 90 degrees,in my head, the remaining area until line AD seemed to be around 45 degrees. So, I simply added 90 and 45 to get 135. That's why I think angle ADE is around 135 degrees. (D.B.T)
ReplyDeleteCA period 1 the angle is 128 degrees. That's because I made a 180 angle and it was too straight so I did 90 degrees but it was too little. if I were to take away 20 degrees each time from 180 I'd slowly line up with all lines. Ending with 128 degrees.
ReplyDelete65 QB per3
ReplyDeleteJ.S. P6
ReplyDeleteThe base angles of an isosceles triangle are equal
and their sum is equal to 130 because the sum of the angles of a triangle is 180. the vertex angle is 50 so 180 - 50 = 130. I also checked this by going onto desmos geometry and using the tools there to help me, which also gave me 130 degrees.
M.S 6
ReplyDeleteThe angle is 65 degrees. I know the base angles of an isosceles triangle are equal while one of them is different. As you already know one of the vertices is 50 degrees. Usually a triangle sums up to 180 degrees. So if we do 180 - 50 i’ll tell us the sum of this isosceles triangle is 130. So the other 2 angles must equal 130 degrees. If you divide 130 by 2 you’ll get 65. Meaning the two angles left are each 65 degrees. So this would mean ADE and BED both equal 65 degrees.
MC Period 3 25 degrees
ReplyDeleteak per 3 the answer is 130 i know this because i took 180 degrees and then i subtracted the 50 degrees and i got 130.
ReplyDeleteAA per 3
ReplyDeleteThe answer is 130 degrees. I found this out by taking 180 degrees and subtracting 50 degrees. From this I simply got the answer.
JC block 3 25
ReplyDeleteThe measure of ADE is 115 degrees.
ReplyDeleteHow doI know?
If we already know that the vertex of ABC is 50 degrees and the interior angle of a triangle is 180, then we know that we have to subtract the vertex angle which is 50 degrees from 180.
180 - 50 = 130
Then we need to find the degrees of the base angles of both triangles by dividing 130 by the 2.
130/ 2 = 65
We already know that the base angles are 65 degrees and the interior angle of a triangle is 180 degrees but we don’t know the measure of ADE, we have to solve.
65 + x = 180
180 - 65 = 115
X = 115
Therefore the measure of ADE is 115 degrees.
LM - P1
ReplyDeleteThe measure of ADE is 115 degrees.
How do I know?
If we already know that the vertex of ABC is 50 degrees and the interior angle of a triangle is 180, then we know that we have to subtract the vertex angle which is 50 degrees from 180.
180 - 50 = 130
Then we need to find the degrees of the base angles of both triangles by dividing 130 by the 2.
130/ 2 = 65
We already know that the base angles are 65 degrees and the interior angle of a triangle is 180 degrees but we don’t know the measure of ADE, we have to solve.
65 + x = 180
180 - 65 = 115
X = 115
Therefore the measure of ADE is 115 degrees.
MR. Period 6.
ReplyDeleteI think the measure of ADE is 25 degrees because d and e are in like the middle of the triangle and if they have the vertex of 50 and they're on the middle and the division of 50 is 25