https://file.aiquickdraw.com/mathbot/file/1729868583408sf6mvb89.jpg

In this image, we see a straight line \( AB \), and points \( D \), \( C \), and \( E \) with angles marked around point \( C \). The goal is to find the value of the angle \( x \).

The angle \( ACD \) is \( 70^\circ \) and the angle \( EBC \) is \( 40^\circ \). Since \( AB \) is a straight line, the sum of all the angles around point \( C \) must add up to \( 180^\circ \) (a property of straight angles).

Thus, we can form the equation:

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

Solving for \( x \):

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

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

\[
x = 70^\circ
\]

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

Would you like any more details, or do you have any questions?

Here are 5 related questions:
1. How would the problem change if the straight line was not present?
2. What if the angle \( DCE \) was given instead of \( ACD \)?
3. Can you calculate the complementary angles to those shown in the diagram?
4. How would the problem change if \( ACD \) was \( 80^\circ \)?
5. What is the sum of all internal angles at a point?

**Tip**: Always remember, angles on a straight line sum up to 180°. This is a key principle in geometry.

Find the value of x based on the diagram, where angles 70° and 40° are given around point C.

Learn how to find the value of x using angles on a straight line with a step-by-step solution. This problem involves calculating the sum of angles around point C, where the sum of 70° and 40° is subtracted from 180°. Suitable for students in Grades 6-8.

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