Question

find the measure of the angle indicated in bold

Answer 1

Answer:

3/2 =x

Step-by-step explanation:

These two angles are interior angles.  They add up to 180 degrees

20x+5 = 24x-1

Subtract 20x from each side

20x-20x+5 = 24x-20x-1

5 = 4x-1

Add 1 to each side

5+1 =4x-1+1

6 =4x

Divide by 4

6/4 = 4x/4

3/2 =x

Answer 2

The measure of the two angles are:  $\mathbf{85^{\circ} and 95^{\circ}}$

• The figure shows two interior angles that lie on the same side of the transversal.

• Both angles are same-side-interior angles.

• Same-side-interior angles are supplementary angles which add up to 180 degrees

• Therefore:

$20x + 5 + 24x - 1= 180$

• Add like terms

$44x + 4 = 180$

• Subtract 4 from both sides

$44x = 180 - 4\\\\44x = 176$

• Divide both sides by 44

$x = 4$

• Find the measure of each angle given in the figure

$20x + 5$

• Plug in the value of x

$20(4) + 5 \\\\= 80 + 5\\\\= 85^{\circ}$

• $24x - 1$

• Plug in the value of x

$24(4) - 1 \\\\= 96 - 1\\\\= 95^{\circ}$

The measure of both angles are $\mathbf{85^{\circ} and 95^{\circ}}$

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