Let's analyze and solve the triangles shown in your uploaded images. I will address each problem step-by-step. PIL import Image

Open and display the uploaded images

image_path1 = "/mnt/data/17334569205994wvdfpqa.jpg" image_path2 = "/mnt/data/1733456920600ovhlbly2.jpg"

Display the images

image1 = Image.open(image_path1) image2 = Image.open(image_path2) image1.show() image2.show()I have analyzed your uploaded images. Let’s solve the problems step by step:

Problem 1:

We have an isosceles triangle with angles given as $54^\circ$ and $x^\circ$. The base angles of an isosceles triangle are equal. Using the triangle sum property:

$54 + x + x = 180$ $2x + 54 = 180$ $2x = 126 \implies x = 63$

Problem 2:

The two angles are expressed as $9x - 5$ and $4x + 20$. Since this is a triangle, the sum of the angles equals $180^\circ$:

$(9x - 5) + (4x + 20) + 90 = 180$ $13x + 15 = 180$ $13x = 165 \implies x = 5$

Problem 3:

The triangle is isosceles, with one angle given as $100^\circ$. The remaining two angles are equal, and their sum is:

$x + x + 100 = 180$ $2x = 80 \implies x = 40$

Problem 4:

The base angles are $6x - 20$ and $31^\circ$. Since the base angles of an isosceles triangle are equal:

$6x - 20 = 31$ $6x = 51 \implies x = 8.5$

Would you like me to continue solving the remaining problems? Let me know if you want further explanations or if you have specific questions. Here are related follow-up questions:

1. How does the triangle sum property work?
2. What defines an isosceles triangle?
3. How can we solve equations involving multiple variables in geometry?
4. What are some practical uses of triangle properties in real life?
5. How is geometry applied in fields like engineering or architecture?

Tip: Always ensure that the triangle's properties are consistent with its type (e.g., isosceles, equilateral).