If ΔPQR ~ ΔXYZ , ∠Q = 50° , ∠R = 70° then ∠X is equal to :a)50°b)60°c)70°d)120°Correct answer is option 'B'. Can you explain this answer?

Question

If &#916;PQR ~ &#916;XYZ , &#8736;Q = 50&#176; , &#8736;R = 70&#176; then &#8736;X is equal to :&#8203;a)50&#176;b)60&#176;c)70&#176;d)120&#176;Correct answer is option 'B'. Can you explain this answer?

Answer

Angle Q = 50
Angle R= 70
Angle p = ?
now
we know that the angle sum property of a triangle is equal to 180 degree
Angle Q + angle R+ angle P = 180
50 + 70 + angle P = 180
120 + angle P = 180
angle P = 180 - 120
-Angle p = 60
as they both are similar so by corresponding parts of similar triangle
Angle P = Angle X
Angle x = 60....

Answer

60 (is the answer )

Answer

You_____ to read regularly

Answer

Since those 2 triangle are similar, angle p = angle x.
therefore by angle sun property,
angle p = angle x = 60

Answer

Given that PQR ~ XYZ, we are asked to find the value of X when Q = 50 and R = 70.

To solve this problem, we need to understand the concept of similarity between two triangles.

Similar Triangles: Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion. In other words, the ratio of the lengths of corresponding sides of two similar triangles is equal.

In triangle PQR and XYZ, we are given that the triangles are similar.

Corresponding Angles:
- Angle P corresponds to angle X
- Angle Q corresponds to angle Y
- Angle R corresponds to angle Z

Corresponding Sides:
- Side PQ corresponds to side XY
- Side QR corresponds to side YZ
- Side PR corresponds to side XZ

Since we are given that Q = 50 and R = 70, we can use the concept of corresponding sides to find the value of X.

Corresponding Sides:
- PQ/XY = QR/YZ = PR/XZ

Plugging in the values, we have:

- PQ/XY = 50/XY
- QR/YZ = 70/YZ

Since the corresponding sides are in proportion, we can equate the two ratios:

50/XY = 70/YZ

To find the value of X, we need to solve for XY.

Cross-multiplying:

50 * YZ = 70 * XY

Simplifying the equation:

XY = (50 * YZ)/70

Given that YZ is a constant, we can substitute the value of YZ with the given value of R:

XY = (50 * 70)/70

Simplifying further:

XY = 50

Therefore, X is equal to 50.

Hence, the correct answer is option B) 60.

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