Determine the measure of angle ACD

Mathematics

2 answers:

nlexa [21]1 year ago

6 0

Answer:

115°

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.

Following this information we can conclude the measure of angle ACD:

40 + 75 = 115

UNO [17]1 year ago

3 0

Answer:

ACD = 115

Step-by-step explanation:

The interior angles of a triangle have to add up to 180, so add 40 and 75 then subtract it from 180.That would cause angle ACB to be 65. Angle ACD and angle ACB have to add up to equal 180. 180-65= 115, so angle ACD = 115.

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The sum of the infinite geometric series is -288.

<h2>Given that</h2>

A finite geometric series with n = 4, a₁ = -144, and r = ½.

<h3>We have to determine</h3>

What is the sum of the infinite geometric series?

<h3>According to the question</h3>

The sum of the infinite is determined by the following formula;

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Substitute all the values in the formula;

$\rm S\infty = \dfrac{a_1(1-r^n)}{1-r}\\\\S\infty = \dfrac{-144 (1- \dfrac{1}{2}^4)}{1-\dfrac{1}{2}}\\\\S \infty = \dfrac{-144 \times \dfrac{15}{16}}{\dfrac{1}{2}}\\\\S \infty = -270$