https://file.aiquickdraw.com/mathbot/file/1726674486125d8639y53.jpg

ABC is an isosceles triangle

What is the size of angle ABC?

____°

In this isosceles triangle \( \triangle ABC \), the two equal sides imply that the angles at points \( A \) and \( C \) (base angles) are also equal. Therefore, \( \angle A = \angle C \).

The given angles in terms of \( x \) are:

\[
\angle A = (9x - 4)^\circ
\]
\[
\angle C = (7x + 12)^\circ
\]

Since \( \triangle ABC \) is isosceles, these two angles are equal:

\[
9x - 4 = 7x + 12
\]

Now, let's solve for \( x \):

\[
9x - 7x = 12 + 4
\]
\[
2x = 16
\]
\[
x = 8
\]

Now substitute \( x = 8 \) back into the expressions for \( \angle A \) and \( \angle C \):

\[
\angle A = 9(8) - 4 = 72 - 4 = 68^\circ
\]
\[
\angle C = 7(8) + 12 = 56 + 12 = 68^\circ
\]

Since the sum of the interior angles of a triangle is always 180°:

\[
\angle ABC + \angle A + \angle C = 180^\circ
\]
\[
\angle ABC + 68^\circ + 68^\circ = 180^\circ
\]
\[
\angle ABC = 180^\circ - 136^\circ = 44^\circ
\]

Thus, the size of angle \( \angle ABC \) is \( 44^\circ \).

Would you like further details or have any questions?

Here are some related questions to expand the concept:

1. What are the properties of an isosceles triangle?
2. How do we calculate the sum of angles in any triangle?
3. Can an isosceles triangle have two angles greater than 90°?
4. What if the angles were in a scalene triangle?
5. How do the angles change if we alter the side lengths?

**Tip:** Always remember that the sum of interior angles of any triangle is always 180°, regardless of its type.

ABC is an isosceles triangle. What is the size of angle ABC?

Learn how to solve for angle ABC in an isosceles triangle where angles A and C are expressed as (9x - 4)° and (7x + 12)°. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation