Question

Construct $∆$ XYZ, in which $\angle$Y = ${58}^{°}$, $\angle$X = ${46}^{°}$ and perimeter of triangle is 10.5 cm.

Answer 1

Steps of construction:
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(1) Draw seg PQ of 10.5 cm length.
(2) Draw a ray making angle of 29° at point P.
(3) Draw another ray making an angle of 23° at point Q.
(4) Name the point of intersection of the two rays as Z.
(5) Draw the perpendicular bisector of seg PZ and seg QZ.
Name the points as Y and X respectively where the perpendicular bisectors intersect line PQ.
(6) Draw seg XZ and seg YZ.

Therefore, △XYZ is the required triangle.