CHITANYA, always designs furniture in a fashionable manner. This time he designed new ladder shaped shoe rack with four parallel racks .For this he took four cuboidal rods each of 120 cm long. Boards were placed at 20 cm, 45cm, 75cm and 110 cm from the top. He set this ladder shape shoe rack as shown in above figure. On basis of figure answer the following questions
Answers
Given : ladder shaped shoe rack with four parallel racks
four cuboidal rods each of 120 cm long. Boards were placed at 20 cm, 45cm, 75cm and 110 cm from the top.
To Find : Measure of angle z
Which property can help him to check that all boards are parallel
Corresponding angle pairs are equal
Sum of corresponding angles must be 180°
Vertically opposite angles are equal
Sum of adjacent angles = 180°
Solution:
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent.
• Alternate angles are congruent. ( Interiors & Exterior both )
• Interior angles are supplementary. ( adds up to 180°)
From given options
Corresponding angle pairs are equal
property can help him to check that all boards are parallel
angle x is corresponding pair with 30°
measure of angle x = 30°
measure of angle z =180° -30° - 30° = 120°
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