Applying the vertical angle theorem, the measure of the missing angles are:
e = 31
f = 72
d = 77
<h3>What is the Vertical Angle Theorem?</h3>
The vertical angles theorem states that two angles that are vertically opposite to each other have equal measures.
Angle e and 31 degrees are vertical angles. Therefore, based on the vertical angles theorem,
e = 31 degrees.
Also, d = 77 degrees [vertical angles theorem].
e + 77 + f = 180 degrees [straight line angles have a sum of 180 degrees].
Substitute the value of e into the equation
31 + 77 + f = 180
108 + f = 180
Subtract 108 from both sides
108 + f - 108 = 180 - 108
f = 72 degrees.
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If there is 8 ice cream sandwiched with 2 pints in each just multiply and it's 16 pints. A strategy you can use is the count on strategy for example -
2,4,6,8,10,12,14,16
Number of ones = 60
Number of twos = 62
Number of threes = 59
Number of fours = 64
Number of fives = 63
Number of sixes = 75
Total even outcomes = total number of two, four and sixes = 62 + 64 + 75 = 201
Total outcomes = 60+62+59+64+63+75= 383
Probability if rolling an even number = 201/383
percentage= 201/383 × 100 = 52.48% ~ 52.5%
Step-by-step explanation:
the scaling ratio is 12/20 = 3/5.
this always applies only to one-dimensional distances, lengths.
the perimeter is calculated as the sum of individual lengths. so while each length is scaled by the same ratio, also the sum is then scaled by that ratio.
p_old = a + b + c
p_new = ra + rb + rc = r(a + b + c) = r×p_old
so, the ratio for the perimeter is also 3/5.
for the area this is a bit different, as an area is always calculated by multiplying 2 lengths (other unscaled factors can be ignored for that consideration of relative change), and that means the scaling ratio has to be multiplied in twice.
a_old = a × b
a_new = ra × rb = r² × a×b = r² × a_old
so, the ratio for the area is
(3/5)² = 9/25
