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3 years ago

8

If two angles are complementary angles and they measure m ∠1=(x + 5) and m∠2=(5x + 13). Find x and the measure for both an

gles.

1 answer:

Korolek [52]3 years ago

6 0

<em>5</em><em>X</em><em>+</em><em>1</em><em>3</em><em>+</em><em>X</em><em>+</em><em>5</em><em>=</em><em>9</em><em>0</em><em>°</em><em>(</em><em>SUM</em><em> </em><em>OF</em><em> </em><em>COMPLEMENTRY</em><em> </em><em>ANGLE</em><em> </em><em>IS</em><em> </em><em>EQUAL</em><em> </em><em>TO</em><em> </em><em>9</em><em>0</em><em>°</em><em>)</em>

<em>6</em><em>+</em><em>1</em><em>8</em><em>=</em><em>9</em><em>0</em><em>°</em>

<em>6</em><em>X</em><em>=</em><em>9</em><em>0</em><em>°</em><em>-</em><em>1</em><em>8</em><em>°</em>

<em>X</em><em>=</em><em>7</em><em>2</em><em>°</em><em>/</em><em>6</em>

<em>X</em><em>=</em><em>1</em><em>2</em><em> </em><em>°</em><em>ANSWER</em>

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Segment addition postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

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Question # 17

<em>Step One: Find the length of PT</em>

Given:

PR = 4 cm
RT = 6 cm

PT = PR + RT [Segment addition postulate]

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PT = 10 cm

<em>Step Two: Find the length of S to PT perpendicularly</em>

According to the diagonal are perpendicular to each other and congruent. Therefore, the length of S to PT perpendicularly is half of the diagonal

Length of Diagonal = 4 cm

4 ÷ 2 = 2 cm

<em>Step Three: Find the area of ΔPST</em>

b = PT = 10 cm

h = S to PT = 2 cm

A = bh / 2

A = (10)(2) / 2

A = 20 / 2

A = 10 cm²

<em>Step Four: Find the length of Q to PT perpendicularly</em>

Similar to step two, Q is the endpoint of one diagonal, and by definition, diagonals are perpendicular and congruent with each other. Therefore, the length of Q to PT perpendicularly is half of the diagonal.

Length of Diagonal = 4 cm

4 ÷ 2 = 2 cm

<em>Step Five: Find the area of ΔPQT</em>

b = PT = 10 cm

h = Q to PT = 2 cm

A = bh / 2

A = (10)(2) / 2

A = 20 / 2

A = 10 cm²

<em>Step Six: Combine area of two triangles to find the total area</em>

Area of ΔPST = 10 cm²

Area of ΔPQT = 10 cm²

10 + 10 = 20 cm²

Hope this helps!! :)

Please let me know if you have any questions

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