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2 years ago

Im so confused please help with 5 and 6

Mathematics

2 answers:

Drupady [299]2 years ago

8 0

Answer:

5)102,78

6)56,56

See THE IMAGE FOR SOLUTION 

Elena-2011 [213]2 years ago

3 0

Answer:

78° and 65°

Step-by-step explanation:

(5)

The 2 angles lie on a straight line and sum to 180° , that is

x + 84 + x + 108 = 180

2x + 192 = 180 ( subtract 192 from both sides )

2x = - 12 ( divide both sides by 2 )

x = - 6

Then

x + 84 = - 6 + 84 = 78°

(6)

the angle opposite 8x is 9x - 7 ( corresponding to the 9x - 7 )

So 8x and 9x - 7are vertical angles and congruent

9x - 7 = 8x ( subtract 8x from both sides )

x - 7 = 0 ( add 7 to both sides )

x = 7

Then

9x - 7 = 9(7) - 7 = 63 - 7 = 56°

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The supplement of an angle is 50 less than 3 times its complement, find the measure of the angle

Lelechka [254]

Answer:

$20^{\circ}$ .

Step-by-step explanation:

Two angles are supplements of one another if their sum is $180^{\circ}$ .

Two angles are complements of one another if their sum is $90^{\circ}$ .

Let $x^{\circ}$ be the measure of the angle in question.

The supplement of this angle would be $(180 - x)^{\circ}$ .

The complement of this angle would be $(90 - x)^{\circ}$ .

According to the question:

$(180 - x) + 50 = 3\, (90 - x)$ .

Solve this equation for $x$ :

$x = 20$ .

Thus, this angle would measure should $20^{\circ}$ .

The supplement of this angle would measure $(180 - 20)^{\circ} = 160^{\circ}$ . The complement of this angle would measure $(90 - 20)^{\circ} = 70^{\circ}$ .

Three times the complement of this angle would be $3 \times 70^{\circ} = 210^{\circ}$ , which is indeed $50^{\circ}$ greater than the supplement of this angle.