Please answer my question as soon as possible by step by step explanation.
Answers
Answer:
(i). x = 32°
Step-by-step explanation:
In (i), the sides containing 32° and x are given to be equal.
∴ x = 32° (angles opposite to equal sides are equal)
As angle y is external angle, 32° + x = y (External angle in a triangle is equal to the sum of its interior opposite angle)
=> 32° + 32° = y = 64°
The line containing y and the line opposite are given to be equal.
Thus, y and its opposite (third) angle are 64°. (Angles opposite to equal sides are equal)
Acc. to ASP (Angle Sum Property) of triangle, sum of angles of a triangle is 180°.
So, y + z + third angle = 180°
=> 64° + z + 64° = 180°
=> z + 128° = 180°
∴ z = 180° - 128° => 52°
∴ x = 32°
y = 64°
z = 52°
(ii) The line containing 35° and the line opposite to it are given to be equal.
∴ Other angle (angle along the lines of angle x) = 35°
As y is external angle, it is equal to the sum of its interior opposite angles.
=> y = 35° + other angle (angle along the lines of x)
∴ y = 35° + 35° => 70°
The line containing y and the line opposite to it are equal.
Thus, y = other angle (angle opposite to x) = 70°
As x is external angle, its sum will be equal to sum of interior opposite angles.
=> x = y + other angle (angle opposite to x)
=> 70° + 70° => 140° = x
∴ x = 140°
y = 70°