Marlene noticed that when a pair of parallel lines was cut by a transversal, two particular vertical angles were reflections of
each other. What can she conclude from this observation?
A. the measures of the angles must be equal.
B.the angles must be complementary.
C.the angles must be supplementary.
D.the measures of the angles must add to 360°.
A. the measures of the angles must be equal.
B.the angles must be complementary.
C.the angles must be supplementary.
D.the measures of the angles must add to 360°.
2 answers:
Answer:
<h2>A. the measures of the angles must be equal.</h2>Step-by-step explanation:
She can conclude that the measure of the angles must be equal, because vertical angles are angles opposite each other when to lines cross, the only thing they have in common is the vertex, when this happens that pair of angles are congruent.
An image is attached to show an example of vertical angles, which are always congruent.
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The surface area of the triangular prism is 828 in².
Solution:
Let the missing length of the triangle be x.
Using Pythagoras theorem,
In right triangle, square of the hypotenuse is equal to the sum of the squares of other two sides.
Subtract 144 on both sides of the equation.
Taking square root on both sides, we get
x = 9
The missing length of the triangle is 9 in.
Area of the front triangle =
= 54 in²
Area of the back triangle =
= 54 in²
Area of the sloping rectangle = 20 × 9
= 180 in²
Area of the back rectangle = 20 × 12
= 240 in²
Area of the base rectangle = 20 × 15
= 300 in²
Total area = 54 in² + 54 in² + 180 in² + 240 in² + 300 in²
= 828 in²
The surface area of the triangular prism is 828 in².