Suppose that a triangle and a rectangle lie in plane. What is the greatest number of points at which they can intersect ?
1 answer:
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Answer:
d
Step-by-step explanation:
We know that diagonals bisect angles of a rhombus, meaning that they split the angles of two equal parts, that opposite angles are equal, and that the angles of a quadrilateral, such as a rhombus, add up to 360 degrees.
Looking at the drawing I uploaded, and taking into account that diagonals bisect angles of a rhombus, we can say that angle x = y and z = 5x-18
Next, given that opposite angles are equal, we can say that angle B = angle D and angle A = angle C. Therefore,
A+B+C+D= 360 (as the angles of a quadrilateral add up to 360)
A + B + A + B = 360 (plugging in A for C and B for D)
2 ( A + B) = 360
A + B = 180
x + y + z + 5x - 18 = 180 (plugging x+y in for A, and z+5x-18 in for B, as x and y make up A and z and 5x-18 make up B)
x+x+5x-18+5x-18 = 180 (because x=y and z=5x-18)
2(x+5x-18) = 180
divide both sides by 2
x+5x-18=90
6x-18=90
add 18 to both sides
6x=108
divide both sides by 6
x = 18
