I need help. One diagram backward Z, has 2|lines intersected by another line. The upper corner on left is 32 degrees. coming down intersecting line, the bottom <Z is outside corner of figure. The other figure is a triangle. Left corner = x, rt. corner =46 degrees , top ?. X complementary to w. y complementary to 54 degrees. Need values of w, x, y, and z. Appreciate help.
To solve this problem, let's break it down step by step:
Step 1: Identify the angles in the backward Z figure.
- The upper corner on the left is given as 32 degrees.
- The bottom angle of the Z (outside corner of the figure) is not provided. Let's call it "z".
Step 2: Identify the angles in the triangle figure.
- The left corner of the triangle is given as "x".
- The right corner of the triangle is given as 46 degrees.
- The top angle of the triangle is not provided. Let's call it "y".
Step 3: Use the properties of complementary angles.
- "x" is complementary to "w".
- "y" is complementary to 54 degrees.
Now, we can solve for the missing angles.
Step 4: Find the value of "z":
- Since the upper corner on the left of the backward Z is 32 degrees, the lower angle (outside corner) of the Z will also be 32 degrees to form a straight line.
- Therefore, "z" is equal to 32 degrees.
Step 5: Find the value of "w":
- Since "x" is complementary to "w", we can use this relationship to solve for "w".
- The sum of complementary angles is 90 degrees.
- Therefore, "w" = 90 degrees - "x".
Step 6: Find the value of "y":
- Since "y" is complementary to 54 degrees, we can use this relationship to solve for "y".
- The sum of complementary angles is 90 degrees.
- Therefore, "y" = 90 degrees - 54 degrees.
Step 7: Find the value of "x":
- We already know that "x" is the left angle of the triangle.
- Therefore, "x" remains as "x".
Step 8: Find the value of "w":
- Substitute the value of "x" from Step 7 into the equation we derived in Step 5: "w" = 90 degrees - "x".
- Therefore, "w" = 90 degrees - "x".
Now, you have the values of "w", "x", "y", and "z".