Since opposite angles on an intersecting line(s) are equal, you already know one of the three angles are 30° because one of the given angles is 30°. To find other two angles, add the two 30°s together to get 60° and subtract that from 360° because all the angles combined have to equal 360°, which is 300°. To get each angle separately, divide 360 by 2, which is 150. Thus, the measure of the other three angles angles are 30°, 150°, and 150°.
is the sum of positive integers between (inclusive) and (inclusive) that are not multiples of and not multiples .
Step-by-step explanation:
For an arithmetic series with:
as the first term,
as the last term, and
as the common difference,
there would be terms, where as the sum would be .
Positive integers between (inclusive) and (inclusive) include:
.
The common difference of this arithmetic series is . There would be terms. The sum of these integers would thus be:
.
Similarly, positive integers between (inclusive) and (inclusive) that are multiples of include:
.
The common difference of this arithmetic series is . There would be terms. The sum of these integers would thus be:
Positive integers between (inclusive) and (inclusive) that are multiples of include:
.
The common difference of this arithmetic series is . There would be terms. The sum of these integers would thus be:
Positive integers between (inclusive) and (inclusive) that are multiples of (integers that are both multiples of and multiples of ) include:
.
The common difference of this arithmetic series is . There would be terms. The sum of these integers would thus be:
.
The requested sum will be equal to:
the sum of all integers from to ,
minus the sum of all integer multiples of between and , and the sum integer multiples of between and ,
plus the sum of all integer multiples of between and - these numbers were subtracted twice in the previous step and should be added back to the sum once.