Question

a pair of same-side interior angles formed have measures of (2x-11) and (9x+6.75). what is the measure of the smaller angle

Answer 1

The measure of smaller angle is: 22.5°

Step-by-step explanation:

When two parallel lines are intersected by a transversal, the pairs of interior angles formed on same side are supplementary angles

So,

The sum of given angles will be 180°

Writing mathematically

$2x-11 + 9x+6.75 = 180\\11x -11+6.75 = 180\\11x -4.25 = 180\\11x = 180 + 4.25\\11x = 184.25\\\frac{11x}{11} = \frac{184.25}{11}\\x = 16.75$

Angle 1:

$2x-11\\= 2(16.75) -11\\=33.5-11\\= 22.5$

Angle 2:

$9x+6.75\\= 9(16.75) + 6.75\\= 150.75+6.75\\=157.5$

Hence,

The measure of smaller angle is: 22.5°

Keywords: Interior angles, supplementary angles

Learn more about interior angles at:

• brainly.com/question/729447
• brainly.com/question/7287774

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