https://file.aiquickdraw.com/mathbot/file/1729868664845btwa7l2v.jpg

To find the value of \( x \) in the given diagram, we can use the fact that the angles on a straight line sum up to 180°. In this case, angles \( \angle DCE \), \( \angle ACD \) (70°), and \( \angle ECB \) (40°) together form a straight line at point \( C \).

Thus, we can set up the equation:

\[
\angle ACD + \angle x + \angle ECB = 180^\circ
\]

Substitute the known values:

\[
70^\circ + x + 40^\circ = 180^\circ
\]

Simplifying:

\[
110^\circ + x = 180^\circ
\]

Now, solve for \( x \):

\[
x = 180^\circ - 110^\circ
\]

\[
x = 70^\circ
\]

Thus, the value of \( x \) is \( 70^\circ \).

Would you like further details or have any other questions?

Here are 5 related questions for further practice:

1. What is the sum of the interior angles of a triangle?
2. How do you calculate supplementary angles?
3. What are vertically opposite angles, and how are they related?
4. If the angle \( \angle DCE \) were doubled, what would \( x \) become?
5. Can you apply the exterior angle theorem to solve for angles in other cases?

**Tip:** Remember, angles on a straight line always add up to 180°, which is key in solving many geometry problems.

Find the value of x in the given diagram, where angle DCE = x, angle ACD = 70°, and angle ECB = 40°.

Learn how to find the value of x using the angle sum on a straight line property in this geometry problem. The solution involves using the supplementary angles theorem. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation