Answer:
x°=60°
y°=60
Step-by-step explanation:
For triangle abd it is ab equilateral triangle which means that all sides are equal.
Total angle in a triangle =180
x+x+x= 180
3x=180
x=60°
For troangle bcd it is an isosceles triangle which means only twi sides are equal
Answer:
We have the equation,
i.e.
i.e.
It is required to find a system of equations having infinite solutions.
We know that,
'When the equations are dependent or their graphs are same, the system of equations has infinite number of solutions'.
So, we can take any equation having same graph as that of .
Let, us take
So, from the graph of these equations below, we get the system of equations having infinite solutions as,
and .
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Answer:
A=80
B=31
C=64
Step-by-step explanation:
A, 69, and b will equal 180 since it forms a straight line
A+69+b=180
to solve for A we subtract 53+47 from 180 and get 80
80+69+b=180
to get B we subtract 80+69 from 180 and get 31
to get c we add 85+b and subtract it from 180 getting c=64
<span>A. triangle P N Q is congruent to triangle N P R by the S A S Congruence Postulate.
Let's take a look at the options and determine which make sense and which doesn't.
A. triangle P N Q is congruent to triangle N P R by the S A S Congruence Postulate.
* This is true. You have a side, a 90 degree angle, and another side. So this is the correct choice.
B. triangle N Q R is congruent to triangle R P N by the S S S Congruence Postulate.
* The problem with this choice is although two triangles are congruent due to the SSS postulate, it's assuming that the diagonals are already congruent. And since our objective is to prove that they're congruent, basing your proof upon their already being congruent is faulty. So this is a bad choice.
C. triangle Q R P is congruent to triangle P N Q by the H L Congruence Theorem.
* The H L Congruence Theorem is true here as well. But it's still assuming that the diagonals (aka the hypotenuse of the right triangle in the H L Congruence Theorem) to already be congruent which is what we're attempting to prove. So this too is a bad choice.
D. triangle Q R P is congruent to triangle P N Q by the S S S Congruence Postulate.
* This is a bad choice for the same reason as option "C" above. Assuming the results of your proof to be true prior to proving it is a bad idea. So this is a bad choice.
Overall, only open "A" works. All of options "B" through "D" assume the congruence of the diagonals prior to actually proving that they're congruent. It's like trying to win an argument with someone by stating "I'll prove that I'm right. Because I'm right, therefore I'm right." Doesn't make a whole lot of logical sense, does it? But that's exactly what "B" through "D" are doing.</span>