1. The value of x in triangle ABC is 27.
2. The value of x in triangle PQR is 4.
3. The value of x is (178 - m)/11 where m is the missing angle measure.
4. The measure of angle 1 = 4x = 4(13) = 52 degrees, and the measure of angle 2 = 10x - 2 = 10(13) - 2 = 128 degrees
5. The number line that best represents the solution to the inequality is a line with an open circle at -11 and shading to the left.
To find the value of x in Triangle ABC, we can use the fact that the sum of angles in a triangle is 180 degrees.
This gives us the equation: 50 + (2x+10) + (3x-15) = 180. Simplifying the equation, we get: 5x + 45 = 180.
Solving for x, we subtract 45 from both sides: 5x = 135, and then divide by 5: x = 27.
In Triangle PQR, if side PQ = PR, then angle P = angle R. We can use this fact to set up an equation: 9x + 21 = 57. Subtracting 21 from both sides: 9x = 36. Dividing by 9: x = 4.
To find the missing angle measure, we can use the fact that the sum of angles in a triangle is 180 degrees.
For the triangle with angle A = (3x+19) and angle B = (8x-17), we have the equation: (3x+19) + (8x-17) + m = 180, where m is the missing angle measure.
Simplifying the equation, we get: 11x + 2 = 180 - m.
Solving for x, we subtract 2 from both sides: 11x = 178 - m, and then divide by 11: x = (178 - m)/11.
In the case of two intersecting lines, we can use the fact that adjacent angles are supplementary (add up to 180 degrees).
For angle 1 = 4x and angle 2 = 10x - 2, we have the equation: 4x + 10x - 2 = 180.
Combining like terms, we get: 14x - 2 = 180. Adding 2 to both sides: 14x = 182.
Dividing by 14: x = 13.
The measure of angle 1 = 4x = 4(13) = 52 degrees, and the measure of angle 2 = 10x - 2 = 10(13) - 2 = 128 degrees.
The inequality -7x + 2x + 25 > 80 can be simplified by combining like terms: -5x + 25 > 80.
Subtracting 25 from both sides: -5x > 55. Dividing by -5 (and reversing the inequality): x < -11.
Therefore, the number line that best represents the solution to the inequality is a line with an open circle at -11 and shading to the left.
The probable question may be:
In triangle ABC, angle A=50 degree, angle B=(2x+10) degree, angle C=(3x-15) degree. Find the value of x.
2. In triangle PQR, angle P=(9x+21)degree, angle Q=57 degree, side PQ=PR. Find the value of x.
3. Set up and solve an equation to find x and the missing angle measure..
m∠A= (3x+19) degree, m∠B=(8x-17) degree.
4. Two lines AM and PQ intersect each other at point U. angle AUP=m∠1=(4x) degree and m∠AUQ=m∠2=(10x-2)degree. find the value of x and measure of angle 1 and 2.
5. Create a number line that best represent the solution to the inequality shown: -7x+2x+25>80