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Question

# A triangle XYZ is constructed such that XY = 2.5 cm, XZ = 5 cm and angle X = 65 degrees. Then triangle ABC is a/an _____.

A
Acute angled scalene triangle
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B
Acute angled isosceles triangle
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C
Right angled triangle
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D
Equilateral triangle
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Solution

## The correct option is A Acute angled scalene triangleStep 1: Draw the base line XY of the length 2.5 cm. Step 2: Measure the angle X with your protractor. Make a mark at 65 degrees and draw a line from X passing through the mark. Step 3: Cut an arc of radius 5 cm on the line passing through the point X. The point where this arc cuts the line is the point Z. Step 4: Draw a line from Y to point Z, to get the required triangle XYZ, as shown below. From the above construction, we see that the measure of angle Y is 85 degrees, measure of angle Z is 30 degrees and the length of side YZ is 4.6 cm. Hence the given triangle is an acute-angled scalene triangle.

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