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(a) Construct triangle 
ABC where angle 
BAC=65^(@) and angle 
ABC=54^(@). 
AB has already been drawn.

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(a) Construct triangle ABC A B C where angle BAC=65 B A C=65^{\circ} and angle ABC=54 A B C=54^{\circ} . AB A B has already been drawn.\newline \mid

Full solution

Q. (a) Construct triangle ABC A B C where angle BAC=65 B A C=65^{\circ} and angle ABC=54 A B C=54^{\circ} . AB A B has already been drawn.\newline \mid
  1. Draw Angle BAC: First, we need to draw angle BACBAC which is 6565 degrees. Use a protractor to measure 6565 degrees from point AA along the pre-drawn side ABAB.
  2. Draw Angle ABC: Next, draw angle ABCABC which is 5454 degrees. Again, use a protractor to measure 5454 degrees from point BB along the pre-drawn side ABAB.
  3. Extend Lines to Form Triangle: Now, extend the lines from the angles BACBAC and ABCABC until they meet at point CC. This will form triangle ABCABC.
  4. Check Angle Sum: Check if the sum of angles BACBAC and ABCABC is less than 180180 degrees before drawing the third side, because the sum of angles in a triangle must be 180180 degrees. 65+54=11965 + 54 = 119, which is less than 180180.
  5. Draw Third Side ACAC: Finally, draw the third side ACAC by connecting the ends of the two angles. Now, triangle ABCABC is constructed.

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