Question

In the diagram, PSR is a straight line. Calculate the value of X and Y.

(easy questions :) HELPPPPPP !!!!​

Answer 1

X= 56 °

Y= 32 °

Hope this helps

Answer 2

x = 56 degrees, y = 32 degrees

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.

• 68 + x + x = 180

Combine like terms.

• 68 + 2x = 180

Subtract 68 from both sides of the equation.

• 2x = 112

Divide both sides the equation by 2.

• x = 56

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:

• ∠PSQ + ∠QSR = 180

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

• 56 + ∠QSR = 180

Subtract 56 from both sides of the equation.

• ∠QSR = 124

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.

• 124 + 24 + y = 180

Combine like terms.

• 148 + y = 180

Subtract 148 from both sides of the equation.

• y = 32

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