Question

2 Construct XYZ, in which < Y = 58° and < X = 46* and perimeter of triangle is 10.5 cm​

Answer 1

Answer:

first draw 10.5 line and go to left and take protractor at center and draw a line in 58 degree and in the right side and keep the protractor at centre and mark 46 degree and your triangle is ready now .

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Answer 2

Step-by-step explanation:

i. As shown in the figure, take point W and V on line YX, such that YW = ZY and XV = ZX ……(i) YW + YX + XV = WV [W-Y-X, Y-X-V] ∠Y + YX + ∠X = WV ……(ii) [From (i)] Also, ∠Y + YX + ∠X = 10.5 cm …..(iii) [Given] ∴ WV = 10.5 cm [From (ii) and (iii)] ii. In ∆ZWY ∠Y = YM [From (i)] ∴ ∠YZW = ∠YWZ = x° …..(iv) [Isosceles triangle theorem] In ∆ZYW, ∠ZYX is the exterior angle. ∴ ∠YZW + ∠YWZ = ∠ZYX [Remote interior angles theorem] ∴ x + x = 58° [From (iv)] ∴ 2x = 58° ∴ x = 29° ∴ ∠ZWY = 29° ∴ ∠W = 29° ∴ Similarly, ∠V = 23° iii. Now, in ∆ZWV ∠W = 29°, ∠V = 23° and WV= 10.5 cm Hence, ∆ZWV can be drawn. iv. Since, ZY = YW ∴ Point Y lies on perpendicular bisector of seg ZW. Also, ZX = XV ∴ Point X lies on perpendicular bisector of seg ZV. ∴ Points Y and X can be located by drawing the perpendicular bisector of ZW and ZV respectively. ∴ ∆XYZ can be drawn. Steps of construction: i. Draw seg WV of length 10.5 cm. ii. From point W draw ray making angle of 29°. iii. From point V draw ray making angle of 23°. iv. Name the point of intersection of two rays as Z. v. Draw the perpendicular bisector of seg WZ and seg VZ intersecting seg WV in Y and X respectively. vi. Join XY and XX. Hence, ∆XYX is the required triangleRead more on Sarthaks.com - https://www.sarthaks.com/849822/construct-xyz-in-which-y-58-x-46-and-perimeter-of-triangle-is-10-5-cm