https://file.aiquickdraw.com/mathbot/file/1727872809300a3q1jeck.jpg

Let's break down and solve this geometry problem.

We are given:
- \( AC \) and \( CD \) are part of a straight line \( ACD \).
- Triangle \( ABC \) is isosceles with \( AB = BC \).
- \( \angle BCD = 138^\circ \), and \( \angle ABC = 28^\circ \).

### Step 1: Understanding the geometry
- Since triangle \( ABC \) is isosceles, the two base angles \( \angle BAC \) and \( \angle BCA \) are equal.
- \( \angle ABC = 28^\circ \) is given.
- We are tasked with finding the value of \( x = \angle BAC \).

### Step 2: Angle sum of a triangle
In triangle \( ABC \), the sum of the interior angles is \( 180^\circ \). This gives us the following equation:
\[
\angle ABC + \angle BAC + \angle BCA = 180^\circ
\]
Since \( \angle BAC = \angle BCA \) (isosceles triangle), we can denote these angles as \( x \). Thus, we have:
\[
28^\circ + x + x = 180^\circ
\]
This simplifies to:
\[
28^\circ + 2x = 180^\circ
\]
\[
2x = 180^\circ - 28^\circ = 152^\circ
\]
\[
x = \frac{152^\circ}{2} = 76^\circ
\]

### Step 3: Using the straight line \( ACD \)
Since \( ACD \) is a straight line, the angles \( \angle BAC \) (or \( x \)) and \( \angle BCD \) are supplementary:
\[
x + 138^\circ = 180^\circ
\]
Substituting \( x = 76^\circ \), we get:
\[
76^\circ + 138^\circ = 214^\circ
\]
This is incorrect based on supplementary angles. Thus, checking the supplementary condition suggests an adjustment is needed. Based on the problem’s conditions, we cross-check for misinterpretations.

In the given figure, ACD is a straight line. ABC is an isosceles triangle. The value of x is:

Find the value of x in an isosceles triangle problem where ACD forms a straight line. The problem involves using the angle sum property and the supplementary angles concept. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation