https://file.aiquickdraw.com/mathbot/file/1726297739847tltpnkgq.jpg

The problem states that \( ABCD \) is a quadrilateral with the following angle measures:

- \( \angle ADC = 70^\circ \)
- \( \angle ACD = 70^\circ \)
- \( \angle ACB = 10^\circ \)
- \( \angle BAD = 110^\circ \)

We are tasked with finding the measure of \( \angle CAB \).

### Step 1: Recognize a triangle
Since quadrilateral \( ABCD \) has angles given at \( C \) and \( D \), the points \( A \), \( B \), and \( C \) form a triangle.

In triangle \( ACB \), we know:
- \( \angle ACB = 10^\circ \)
- \( \angle ACD = 70^\circ \) (which contributes to angle \( A \))

### Step 2: Apply triangle sum property
The sum of the interior angles of any triangle is \( 180^\circ \).

Let \( \angle CAB = x \).

In \( \triangle ACB \):
\[
x + 10^\circ + 70^\circ = 180^\circ
\]
\[
x + 80^\circ = 180^\circ
\]
\[
x = 180^\circ - 80^\circ = 100^\circ
\]

Thus, the measure of \( \angle CAB \) is \( 100^\circ \).

Would you like further details or have any questions?

### Related Questions:
1. What is the sum of the interior angles in any quadrilateral?
2. How do you calculate the missing angle in a triangle?
3. What is the exterior angle theorem for triangles?
4. Can you solve for the other interior angles of quadrilateral \( ABCD \)?
5. How does knowing the properties of triangles help in solving quadrilateral problems?

### Tip:
In any polygon, the sum of the interior angles is given by \( 180(n-2) \), where \( n \) is the number of sides.

Let ABCD be a quadrilateral with ∠ADC = 70°, ∠ACD = 70°, ∠ACB = 10°, and ∠BAD = 110°. The measure of ∠CAB (in degrees) is:

Solve the problem of finding the measure of ∠CAB in quadrilateral ABCD with angles ∠ADC = 70°, ∠ACD = 70°, ∠ACB = 10°, and ∠BAD = 110°. This solution uses geometric concepts, including the triangle sum theorem and angle properties, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation