When two angles are a linear pair, the sum of their measures is 180°:
∡1 + ∡ 2 = 180°
Substituting the expressions for the angles, you get:
<span>5y − 8 + 12 + 6y = 180
Solve for y:
11y = 176
y = 176/11
Now, substitute this value in the expression for </span>∠2, which is the one we are interested in:
∡2 = 12 + 6y = 12 + 6×(<span>176/11) = 108°
When two angles are vertical angles, it means that they share the same vertex and they have the same measure, therefore:
</span>∡3 = ∡2 = 108°
Hence, the correct answer is <span>C) 108°. </span>
Answer:
n(U) = n(AUB) + n(AUB)'
Step-by-step explanation:
The cardinality of the universal set will be to add the cardinalities of both the union of A and B i.e (A U B) and and the compliments of A and B i.e n(AUB)'
Answer:
554400
Step-by-step explanation:
To answer this question, we use combination as we are just interested in selection rather Than arrangement.
Beyonce songs ; 3 from 8 = 8C3
Justin ; 4 from 12 = 12C4
Drake ; 2 from 5 = 5C2
Version of happy birthday = 1 from 2 = 2C1
Recall :
nCr = n! ÷ (n-r)!r!
However, the answers can also be obtained using a calculator :
8C3 * 12C4 * 5C2 * 2C1 = 554400 different mix
Answer:
b
Step-by-step explanation: