Math, asked by jenniekim46, 1 month ago

pls give step by step explanation

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Answered by jettylasya1521
1

Step-by-step explanation:

first add 50 and 70 and you will get the value ok ? and it is 120 and if you substract it it is 20 check it yourself you need to know the answer your self but u told you the step ok ?

make sure youn answer my question ok ?

Answered by whamwham
2

We are given that PQRS is a parallelogram. Let us begin by finding the measure of ∠TRQ.

As PQRS is a parallelogram, PQ║SR. When a transversal cuts two parallel lines, the corresponding angles are equal. Then ∠RSP = ∠TRQ since they are corresponding angles. So, ∠TRQ = 50°.

(Alternative method to find ∠TRQ:

Adjacent angles in a parallelogram are supplementary.

Therefore,

⇒ ∠QRS + ∠RSP = 180°

⇒ ∠QRS + 50 = 180

⇒ ∠QRS = 180 - 50

⇒ ∠QRS = 130°

∠TRQ and ∠QRS are also supplementary since they form a linear pair. So,

⇒ ∠TRQ + ∠QRS = 180°

⇒ ∠TRQ + 130 = 180

⇒ ∠TRQ = 180 - 130

⇒ ∠TRQ = 50° )

Now we have the measures of two of the three angles in triangle QTR:

  • ∠TRQ = 50°
  • ∠RQT = 70°

To find x or angle QTR, we can use the angle sum property of triangles. It states that the sum of all interior angles of a triangle is 180°. So,

⇒ ∠QTR + ∠TRQ + ∠RQT = 180°

⇒ x + 50 + 70 = 180

⇒ x + 120 = 180

⇒ x = 180 - 120

x = 60°

Therefore the value of x is 60 degrees.

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