Perpendicular lines form angles

7. TOWERS A lookout tower sits on a network of struts and posts. Leslie measured two angles on the tower. If m∠1=7x-7°, m∠2=4x+2

yaroslaw [1]

The angles in a triangle add up to 180 degrees

The measure of $\mathbf{\angle 1 }$ is $\frac{1162}{13}$

The given parameters are:

$\mathbf{\angle 1 = 7x - 7}$

$\mathbf{\angle 2 = 4x + 2}$

$\mathbf{\angle 3 = 2x + 6}$

The angles form a triangle.

So, we have:

$\mathbf{\angle 1 + \angle 2 + \angle 3 = 180}$

This gives

$\mathbf{7x - 7 + 4x + 2 + 2x + 6 = 180}$

Collect like terms

$\mathbf{7x + 4x + 2x = 180 + 7 - 2 - 6}$

$\mathbf{13x = 179}$

Divide by 13

$\mathbf{x = \frac{179}{13}}$

Substitute $\mathbf{x = \frac{179}{13}}$ in $\mathbf{\angle 1 = 7x - 7}$

So, we have:

$\mathbf{\angle 1 = 7 \times \frac{179}{13} - 7}$

$\mathbf{\angle 1 = \frac{1253}{13} - 7}$

So, we have:

$\mathbf{\angle 1 = \frac{1253 - 13 \times 7}{13}}$

$\mathbf{\angle 1 = \frac{1162}{13}}$

Hence, the measure of $\mathbf{\angle 1 }$ is $\frac{1162}{13}$

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6 0

3 years ago

Angle x and angle y are complementary. Angle x is supplementary to a 128 degree angle. What are the measures of angle x and angl

White raven [17]

The measurement of angle x is 52° and y is 38°

Step-by-step explanation:

Let us define supplementary and complementary angles first.

Supplementary angles is pair of angles whose sum is 180°

While complementary angles sum up to 90°

Given

That x and y are complementary and x is supplementary to 128.

This means that sum of x and 128 is 180°

So,

$x+128 = 180\\x = 180 - 128\\x = 52$

x = 52°

It is also given that x and y are complementary which means that

$x+y=90\\52+y = 90\\y = 90-52\\y = 38$

Hence,

The measurement of angle x is 52° and y is 38°

Keywords: Supplementary angles, complementary angles

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3 0

3 years ago

Explain how to round 14 5/6 to the nearest whole number, using the number line as a tool. Use complete sentences in your answer.

tatuchka [14]

Answer:

15

Step-by-step explanation:

We know that a half is equal to 3/6. Therefore 5/6 is higher up on the number line than 0.5, and it should be rounded up

4 0

3 years ago

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Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 2p − 8 < 5p + 4 true.

Alika [10]

The set S:{ - 2 , - 3 } will make the inequality 2p - 8 < 5p + 4 true

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

The set S : { - 2 , - 3 , - 4 , - 5 }

The inequality relation is 2p - 8 < 5p + 4

Now , substituting the value from set S in the inequality , we get

When p = - 2 :

2p − 8 < 5p + 4

2(-2) − 8 < 5(-2) + 4

-4 − 8 < -10 + 4

-12 < -6 TRUE

When p = - 3

2p − 8 < 5p + 4

2(-3) − 8 < 5(-3) + 4

-6 − 8 < -15 + 4

-14 < -11 TRUE

When p = - 4

2p − 8 < 5p + 4

2(-4) − 8 < 5(-4) + 4

-8 − 8 < -20 + 4

-16 < -16 FALSE

When p = - 5

2p − 8 < 5p + 4

2(-5) − 8 < 5(-5) + 4

-10 − 8 < -25 + 4

-18 < -21 FALSE

Therefore , the value of p = - 2 , - 3 will satisfy the given inequality relation

Hence , the set S:{ -2,-3 } is the solution

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3 0

1 year ago

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String A is 1 yard shorter than string B. String C is 1 ft 8 inches shorter than string B.

pentagon [3]

Let the length of string A be x
it is 1 yard = 3 ft shorter than string B
so length of string B = x+3

String C is 1ft 8 inches shorter than B,
so C = x+ 1ft 8 inch = x+ 1+ 2/3 ft.

Total of A +B+C = 13ft 4inch = 13 + 1/3 ft.

x + x+3 + x+1+2/3 = 13 + 1/3
3x + 4 + 2/3 -1/3 = 13
3x = 13 - 4- 1/3
3x = 9 -1/3
x = 3 -1/9
x = 3ft - 12/9 inches = 3 ft - 4/3 inches
x = 2.889 ft

3 0

4 years ago