prove that in a star angle A +angle B+angle C +angle D + angle E = 2 right angles
Answers
Step-by-step explanation:
Actually in a equlateral triangle all the sides and angles are equal. One side of an equlateral is 60 degree so when 6 sides are are multiplied by 60 we will get 360 degree . This figure is a compination of 2 triangles because of angle sum property one triangle is equal to 180 degree. So 2 triangle is equals to 360 degrees.
In △ACE, By angle Sum property of triangle∠A
+∠C+∠E=180° ...(1)Similarly, in △BDF∠B
+∠D+∠F=180° ...
(2)Adding (1) and (2), we get∠A+∠B+∠C+∠D
+∠E+∠F=360°
Hope it helps you.
Thank you
Answer:
Look down for detailed explanation.
Step-by-step explanation:
There can be two cases. One, where the pentagon connecting all five triangles is a regular pentagon (a regular pentagon will have all sides and angles measuring the same). Another case is when the pentagon is irregular.
First case:
We can prove congruency of the triangles by using the ASA congruency criterion. As we know that the pentagon is a regular shaped one, it also means that the base of each triangle will be of the same length. Now, we need angles. We can find that every angle measures the same because they are VOAs (vertically opposite angles). VOAs in every case measure the exact same and thus, congruency is proven. Now that we know that all these triangles measure the same, we can make a statement that the angles A, B, C, D & E measure the same (through CPCT, corressponding parts of congruent triangles.)
As all of the angles in question measure the same, we can take the common measurement of these angles as "x".
As per the question,
angle A+ angle B+ angle C+ angle D+ angle E = 180 degrees.
(now use x instead of the angles' names)
x+x+x+x+x = 180°.
5x = 180°.
x = 180/5
x = 36°.
Now that we know the measurement, proving becaomes an easy task.
We now use the measurement of x in place of x.
36+36+36+36+36 = 180°
180 = 180°. THUS, PROVEN.
(refer to the first two pictures for clearer understanding.)
Second case:
In a case where you don't know whether your pentagon is regular or irregular or if it is irregular, do the following.
You will have to take certain triangles into account for this one. The triangles you will be using are named as follows. (refer to picture three for drawing and naming of triangles.) Once you know what triangles you are looking at, make it easier by freeing the triangles by using FBD (free body diagrams, where you take out the required diagram and put it in free space for better analysis)
