Answer:
Step-by-step explanation:
Let the quotient be represented by 'Q'.
Given:
The difference of a number 'y' and 16 is 
Quotient is the answer that we get on dividing two terms. Here, the first term is 40 and the second term is . So, we divide both these terms to get an expression for 'Q'.
The quotient of 40 and is given as:
Now, we need to find the quotient when 
. Plug in 20 for 'y' in the above expression and evaluate the quotient 'Q'. This gives,
Therefore, the quotient is 10, when the value of 'y' is 20.
We have the following:
solving for x
The solution of x is equal to 28, therefore 12 is not a solution of the equation
<h3>
Answer: 133</h3>
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Explanation:
The quickest way to get this answer is to add the angles given to get 87+46 = 133
This is through the use of the remote interior angle theorem.
Note how the angles 87 and 46 are interior, or inside the triangle. And also, they are not adjacent to the exterior angle we want to find. So that's where the "remote" portion comes in.
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The slightly longer method involves letting x be the measure of the missing interior angle of the triangle.
The three interior angles add to 180
87+46+x = 180
133+x = 180
x = 180 - 133
x = 47
The missing interior angle of the triangle is 47 degrees.
Angle 1 is adjacent and supplementary to this 47 degree angle, so,
(angle1)+(47) = 180
angle1 = 180-47
angle1 = 133 degrees
This example helps confirm that the remote interior angle theorem is correct.
Answer:
if two sides and the included angle of one triangle are congruent to two sides and the angle of another triangle, then these two triangles are congruent.
If two triangles share two pairs of corresponding congruent sides are congruent and their included angle is also congruent, then these two triangles are congruent.
If any two sides and angles included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by the SAS rule.
