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Olenka [21]
2 years ago
7

An angle measures 51.4° less than the measure of its complementary angle. What is the measure of each angle?

Mathematics
1 answer:
kap26 [50]2 years ago
5 0

Answer:

70.7 deg, 19.3 deg

Step-by-step explanation:

The sum of the measures of complementary angles is 90 deg.

One angle measures x.

The other angles measures 51.4 deg less than x, or x - 51.4.

The sum of their measures equals 90.

x + x - 51.4 = 90

2x - 51.4 = 90

2x = 141.4

x = 70.7

x - 51.4 = 70.7 - 51.4 = 19.3

Answer: 70.7 deg, 19.3 deg

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If the perpendicular bisector of one side of a triangle goes through the opposite vertex, then is the triangle isosceles?
Ne4ueva [31]

Answer:

True

Step-by-step explanation:

The perpendicular bisector of the opposite side to the vertex bisects the angle at the vertex into two equal parts and also bisects the triangle into two equal parts.

Let A be the angle at the vertex, then assume that the angle is an isosceles triangle with base angles B.

We need to show that A = 180 - 2B for an isoceles triangle

The perpendicular bisector bisects A into two so the new angle in the vertex one half of the bisected triangle is A/2.

Since this half triangle is a right-angled triangle, the third angle in it is 90.

So, A/2 + B +  90 = 180 (Sum of angles in a triangle)

subtracting 90 from both sides, we have

A/2 + B + 90 - 90 = 180 - 90

A/2 + B = 90

subtracting B from both sides, we have

A/2 + B = 90

A/2 = 90 - B

multiplying through by 2, we have

A = 2(90 - B)

A = 180 - 2B

Since A = 180 - 2B, then our triangle is an isosceles triangle.

7 0
3 years ago
Please help this is timed
elena-14-01-66 [18.8K]

Answer:

option d is correct

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6 0
3 years ago
Read 2 more answers
Solve the following system of linear equations: 3x1+6x2+6x3 = -9 -2x1–3x2-3x3 = 3 If the system has infinitely many solutions, y
choli [55]

Answer:

The set of solutions is \{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number}  \}

Step-by-step explanation:

The augmented matrix of the system is \left[\begin{array}{ccccc}3&6&6&-9\\-2&-3&-3&3\end{array}\right].

We will use rows operations for find the echelon form of the matrix.

  • In row 2 we subtract \frac{2}{3} from row 1. (R2- 2/3R1) and we obtain the matrix \left[\begin{array}{cccc}3&6&6&-9\\0&1&1&-7\end{array}\right]
  • We multiply the row 1 by \frac{1}{3}.

Now we solve for the unknown variables:

  • x_2+x_3=-7, x_2=-7-x_3
  • x_1+2x_2+2x_3=-2, x_1+2(-7-x_3)+2x_3=-2 then x_1=12

The system has a free variable, the the system has infinite solutions and the set of solutions is \{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number}  \}

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Answer:

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Step-by-step explanation:

hope it helped!!!

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Is c=0.6n an example of a proportional relationship?
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Yes it is!!!!!!!!!!!!!!!!!!!!!

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