Let's begin noting that a triangle is isosceles if and only if two of its angles are congruent. We can thus find the angle <ABP, recalling that the sum of the interior angles of a triangle is equal to 180°.

Finally, let point K be the intersection between segments BC and PQ, and let's note that the triangle PQB is a right isosceles triangle, since all the angles in a square are equal to 90°, and the two triangles APB and BQC are congruent.
Therefore, the angle BKQ is equal to 180-50-45=85°.
Of course angle BKP=180-85=95°.
Hope this helps :)
Answer:
Therefore, the possible lengths (in whole inches) for the third side is
9 inches < x < 45 inches
Step-by-step explanation:
For the above question, we have a rule, the sum of the length of any two sides of the triangle must be greater than the length of the third side.
Hence:
She has two sides of length 18 inches and 27 inches
Let the third side = x
Hence:
a) 18 + 27 > x
45 > x
b) 18 + x > 27
x > 27 - 18
x > 9
Therefore, the possible lengths (in whole inches) for the third side is
9 inches < x < 45 inches
Answer:
A) x = 6
Step-by-step explanation:
4x - 2x + 6 = x + 12
Combine like terms
2x +6 = x+12
Subtract 6 from each side
2x+6-6 = x+12-6
2x = x+6
subtract x
2x-x = x+6-x
x = 6
First one: divide multiply 2(1x) which would equal 2x then do 2*3 then u would subtract 5 which should get you to the simplified form 2x+1
Second one: do 3(1x) which would equal 3x then do 7*3 which would equal 21 than do plus 3x which should get you to the simplified form of 6x+21
Third one: Do 4(1x) which equals 4x than do 4*2 which equals 8 than plus eight which should get you to the simplest form of 4x+16
Fourth one: do 4(1x) which would equal 4x then do 4*1 which equals 4 than subtract 6 which should get you to the simplest form of 4x-2
Fifth one: do 2(3x) which equals 6x then do 2*2 which equals 4 than subtract 5x which should get you to the simplest form of x+4
Sixth one: do 5(1x) which equals 5x than do 5*-4 which equals -20 than add 10 which gets you to the simplest form of 5x-10
Let the width be X
Then the length is X + 70
The perimeter is the sum of all sides
There are 2 widths (left side and right side) and 2 lengths (top and bottom)
Perimeter = 2 * width + 2 * length
Perimeter = 2 * X + 2 * (X+70)
Perimeter: 2 X + 2 X + 140 = 380
4 X = 380-140
4 X = 240
X = 240 / 4
X = 60
Width = 60 - the smaller of two sides
Length = X + 70 = 60 + 70 = 130 - the larger of two sides
Check:
<span>
2 * 60 + 2 * 130 = 380 </span>