The picture is not drawn to scale. A right triangle with Angles measuring A degrees and B degrees as the additional angles. Find the value of x in the expressions if A=3x 51 and B=6x−15 (5 points)

7 answers

To solve the problem, we can set up an equation using the fact that the sum of the angles in a triangle is always 180 degrees.

In this case, the two additional angles are A and B. Since A = 3x + 51 and B = 6x - 15, we can write the equation as:

A + B + 90 = 180

Substituting the expressions for A and B, we get:

(3x + 51) + (6x - 15) + 90 = 180

Combining like terms, we have:

9x + 126 = 180

Subtracting 126 from both sides, we get:

9x = 54

Dividing both sides by 9, we find:

x = 6

Therefore, the value of x is 6.
answer??
Apologies for the confusion. The value of x in the expressions is 6.
The image is not drawn to scale. A right triangle with a ray extending off of the vertical leg. Angle measurements of A degrees inside the triangle adjacent to an angle measurement of C degrees outside the triangle. Angle measurement of B degrees is there too. Find the value of B if C=106° (5 points)
To solve the problem, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

In this case, we have angle C, which is given as 106 degrees. And we are also given that it is adjacent to angle A inside the triangle.

Since we have a right triangle with angle A, it means that the other acute angle, which is angle B, is equal to 90 degrees.

Since the sum of the angles in a triangle is 180 degrees, we can set up the equation:

A + B + C = 180

Substituting the known values, we get:

A + 90 + 106 = 180

Combining like terms, we have:

A + 196 = 180

Subtracting 196 from both sides, we get:

A = 180 - 196

Simplifying, we have:

A = -16

Therefore, angle B would have a value of 90 degrees, as it is a right angle.
answer?
My apologies for the incorrect answer. Let's solve the problem correctly:

Given that angle C is 106 degrees and it is adjacent to angle A inside the triangle.

Since we have a right triangle, angle B is the remaining angle.

Since the sum of the angles in a triangle is 180 degrees, we can set up the equation:

A + B + C = 180

Substituting the known values, we get:

A + B + 106 = 180

Combining like terms, we have:

A + B = 74

Since angle A is adjacent to angle C inside the triangle, their sum is 180 degrees:

A + C = 180

Substituting the known values, we get:

A + 106 = 180

Simplifying, we have:

A = 180 - 106

A = 74

Using this value of A, we can substitute it back into the equation for A + B:

74 + B = 74

B = 0

Therefore, the value of angle B is 0 degrees.