Math / Geometry

QuestionFind the value of $x$ in the figire ab

Studdy Solution

STEP 1

1. The sum of angles in a triangle is $180^\circ$ .
2. The angles around a point sum to $360^\circ$ .
3. The problem involves using angle properties in triangles and intersecting lines.

STEP 2

1. Analyze the given angles and relationships in the triangle.
2. Use angle sum properties to find unknown angles.
3. Calculate the value of $x$ .

STEP 3

Identify the known angles in the triangle and the relationships between them. We have: - $\angle DAE = 70^\circ$ - $\angle ABE = 60^\circ$ - $\angle EBC = 60^\circ$ - $\angle ADB = 40^\circ$

STEP 4

Use the angle sum property in $\triangle ABE$ to find $\angle AEB$ . Since $\angle ABE = 60^\circ$ and $\angle ADB = 40^\circ$ , we have:
$\angle AEB = 180^\circ - \angle ABE - \angle ADB$ $\angle AEB = 180^\circ - 60^\circ - 40^\circ$ $\angle AEB = 80^\circ$

STEP 5

Now, use the angle sum property in $\triangle AED$ to find $x = \angle AED$ . We know: - $\angle DAE = 70^\circ$ - $\angle AEB = 80^\circ$
Since $\angle AED = x$ , we have:
$\angle AED + \angle DAE + \angle AEB = 180^\circ$ $x + 70^\circ + 80^\circ = 180^\circ$ $x + 150^\circ = 180^\circ$ $x = 180^\circ - 150^\circ$ $x = 30^\circ$
The value of $x$ is:
$\boxed{30^\circ}$

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