2 lines intersect to form 4 angles. Clockwise, from top left, the angles are: x degrees, 105 degrees, z degrees, y degrees. Which equations are true for the values of x, y, and z in the figure? Select all that apply. x° + 105° = 180° x° = z° 105° – y° = 90° x° + y° + z° = 180° 180° – z° = y° x° + y° = 105°
Answers
Given:
We have been given that two lines intersect to form four angles and the angles have been marked as
x° + 105° = 180°
x° = z°
105° – y° = 90°
x° + y° + z° = 180°
180° – z° = y°
x° + y° = 105°
To find:
We have to find which relation among them is correct or true.
Solution:
For finding the correct relation let us check each relation one by one and state if it satisfies then why or else why not.
So,
1.
x° + 105° = 180°
The above statement is true. [Sum of angles in a straight line are equal to 180°]
2.
x° = z°
The above statement is true. [Vertically opposite angles]
3.
105° – y° = 90°
The above statement is false. [There will not be any such relation in 105° and y°]
The correct relation will be 105° + y° = 180° [Sum of angles in a straight line]
4.
x° + y° + z° = 180°
The above statement is false. [There will not be any such relation between x°, y° and z°]
5.
180° – z° = y°
The above statement is true. [As y° + °z = 180°]
6.
x° + y° = 105°
The above statement is false. [Because x° + y° = 180°]
Answer
A, B, E
Step-by-step explanation:
I did is on the test and the correct answers were
A: x° + 105° = 180°
B: x° = z°
E: 180° – z° = y°