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svet-max [94.6K]
3 years ago
5

The measure of one angle is eleven more than four times a number. Another angle is twice the first angle’s measure. The sum of t

he measures of the angles is 195° What is the measure of each angle in degrees ?
Mathematics
1 answer:
hammer [34]3 years ago
6 0

The measure of first angle is 65 degrees and measure of second angle is 130 degrees

<em><u>Solution:</u></em>

Let "x" be the number

<em><u>The measure of one angle is eleven more than four times a number</u></em>

Measure of first angle = 11 + 4(x)

Measure of first angle = 11 + 4x

<em><u>Another angle is twice the first angle’s measure</u></em>

Measure of second angle = twice the measure of first angle

Measure of second angle = 2(11 + 4x)

<em><u>The sum of the measures of the angles is 195 degrees</u></em>

Measure of first angle + Measure of second angle = 195

11 + 4x + 2(11 + 4x) = 195

11 + 4x + 22 + 8x = 195

12x + 33 = 195

12x = 195 - 33

12x = 162

x = 13.5

<em><u>Thus, measures of each angle are:</u></em>

Measure of first angle = 11 + 4x = 11 + 4(13.5) = 11 + 54 = 65

Measure of second angle = 2(11 + 4x) = 2(11 + 4(13.5)) = 130

Thus measure of first angle is 65 degrees and measure of second angle is 130 degrees

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Step-by-step explanation:

Because MK is a diameter, then angle L is a right angle. We already know that the measure of angle K is 50, so the measure of angle M has to be 40 because of the triangle angle-sum theorem. The rule for inscribed angles and the arcs they cut off is that the angle is half the measure of its intercepted arc or, likewise, the arc is twice the measure of the angle that cuts it off. Since arc LK is across from angle M and is cut off by angle M, then arc LK is twice the measure of angle M, and is 80. That's the same reason why angle L is 90; arc MK is a semi-circle, with a degree measure of 180, and angle L is half of that.

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