Well, one angle has one share of the linear angle, and the other one has five shares. All together, they add up to six shares of the linear angle.
BUT ... a linear angle adds up to 180°. So each share must be (180°/6) = 30°.
The smaller one (one share) is 30°, and the larger one (5 shares) is 150°.
Question 1:
We can use the rule of exterior angle of triangle, where the exterior angle is equal to the sum of the other 2 interior angles of the triangle except for the adjacent one.
So, we can calculate angle 1 by adding up the 2 given angles.
Angle1 = 62° + 57°
=119°
=answer C.
Question 2:
We can also apply the rule above, but first we have to calculate the remaining angle of the triangle first.
For this, we have to use the angle sum of triangle. All 3 interior angles of triangle should add up to 180°.
Let that remaining angle be x.
X = 180° - 62° - 57°
X=61°
Now we can apply the rule of exterior angle of triangle.
Angle 1 = 62° + 61°
=123°
=answer D.
True.
Let p1 and p2 be the two parallel planes. Let n1 be the normal vector of plane p1 (which is a vector perpendicular to the plane). If p2 is parallel to p1, then n1 is also a normal vector for p2.
Let p3 be the third secant plane, and n3 be its normal vector.
The direction vector of the intersection line of two planes is given by the cross products of their normal vectors (this is due to the fact that the cross product of two vectors is orthogonal two both of them, and that the direction vector of the intersection must be orthogonal two both normal vectors). So, the direction vectors of the two lines are:
v1 = n1 × n3
v2 = n1 × n3
The are equal. Hence, the lines are parallel.
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A quarter = 0.25......200 quarters = 200(0.25) = $ 50
a dime = 0.10...150 dimes = 150(0.10) = $ 15
a penny = 0.01....300 pennies = 300(0.01) = $ 3
for a total of : 50 + 15 + 3 = $ 68
