Question

In the figure 3 given below AB||CD find the values of x, y and z​

Answer 1

according to angle sum PROPERTY of TRIANGLE

42⁰ + 24⁰ + 3rd angle = 180⁰

3rd angle = 114 ⁰.......1

now y + z + 3rd angle of this TRIANGLE = 180⁰............EQUATION A

3rd angle of this TRIANGLE + 3rd angle of ist one = 180⁰

becoz linear angles

3rd angle of this triangle + 114⁰( from ist EQUATION) = 180⁰

3rd angle of this TRIANGLE = 180⁰_144⁰=66⁰......2

as in this TRIANGLE sides are equal

so y = 66⁰.

...angles opposite to equal sides are equal. ..

y + z + 66⁰ =180⁰

angle sum PROPERTY of a TRIANGLE

y+z = 114⁰..............3

66⁰ +z = 144⁰

z= 88⁰

also x = 42⁰ ( alternate interior angles)..