In the diagram, PSR is a straight line. Calculate the value of X and Y. (easy questions :) HELP

x = 56 degrees, y = 32 degrees

Step-by-step explanation:

The Isosceles Triangle Theorem (ITT) tells us that if there are two sides of a triangle that are congruent, then the base angles of this triangle are congruent (angles opposite the congruent sides).

Let's focus on Triangle PQS first. We have the acute angle 68° and want to find x. Due to the ITT, we know that the other missing angle must also equal x.

Therefore, we can create an equation where the interior angles of Triangle PQS will add up to 180, because all interior angle measures of a triangle add up to 180 degrees.

Combine like terms.

Subtract 68 from both sides of the equation.

Divide both sides the equation by 2.

We have found that x = 56 degrees, and now we need to find y. We can do so by using the information we have already found. Since we have found the two angles x of Triangle PQS, we can find ∠QSR in Triangle QSR by using the idea that angles that make up a straight line must add up to 180 degrees.

Therefore:

We have found that ∠PSQ = 56, so substitute this value into the equation.

Subtract 56 from both sides of the equation.

Now we can use the fact that all interior angle measurements of a triangle add up to 180 degrees, and since we have 2 angle measures of Triangle QSR, we can create an equation to solve for y.

Combine like terms.

Subtract 148 from both sides of the equation.

We have found x = 56 degrees and y = 32 degrees.

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.