Answer:
∠ A ≅ ∠ E
∠ K = 60°
Step-by-step explanation:
Part 1.
Given that ABCD ≅ EFGH.
Whenever a quadrilateral is congruent to another, and we write the congruency in symbol, then the order of congruency with respect to angles and sides are maintained in the symbol.
That means if ABCD ≅ EFGH, then ∠ A ≅ ∠ E, ∠ B ≅ ∠ F and so on.
Therefore, in this case, ∠ A ≅ ∠ E (Answer) {It is also shown in the diagrams}
Part 2.
Given that, Δ EFG ≅ Δ KLM
Hence, ∠ E ≅ ∠K, ∠ F ≅ ∠ L, and ∠ G ≅ ∠ M
It is also given that ∠ F = 35° and ∠ G = 85°
So, ∠ E = 180° - ∠ F - ∠ G = 180° - 85° - 35° = 60°
Since, ∠ E = ∠ K,
So, ∠ K = 60°. (Answer)
subtract 3 from both sides:
Multiply both sides by 2:
Subtract 3 from both sides:
Change sign to both sides (this implies that you should also change the inequality sign):
Answer:
The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.
Step-by-step explanation:
From statement we know all sides of the triangle (
, 
, 
), but all angles are unknown (
, 
, 
). (Please notice that angles with upper case letters represent the angle opposite to the side with the same letter but in lower case) From Geometry it is given that sum of internal angles of triangles equal 180º, we can obtain the missing information by using Law of Cosine twice and this property mentioned above.
If we know that 
, 
and 
, then the missing angles are, respectively:
Angle A
(1)
![A = \cos^{-1}\left[\frac{16^{2}+11^{2}-19^{2}}{2\cdot (16)\cdot (11)} \right]](https://tex.z-dn.net/?f=A%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B16%5E%7B2%7D%2B11%5E%7B2%7D-19%5E%7B2%7D%7D%7B2%5Ccdot%20%2816%29%5Ccdot%20%2811%29%7D%20%5Cright%5D)
Angle B
(2)
![B = \cos^{-1}\left[\frac{19^{2}+11^{2}-16^{2}}{2\cdot (19)\cdot (11)} \right]](https://tex.z-dn.net/?f=B%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B19%5E%7B2%7D%2B11%5E%7B2%7D-16%5E%7B2%7D%7D%7B2%5Ccdot%20%2819%29%5Ccdot%20%2811%29%7D%20%5Cright%5D)
Angle C
The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.
Angles that combine to make a straight line add up to __180__ degrees.
I hope this helps! :)
