Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Browse grades and teaching videos01 · Read and understand
What you will learn
- Identify the angles opposite equal sides.
- Use the 180° triangle total.
- Find an exterior angle on a straight line.
Before you start
Subtracting and dividing positive numbers; understanding an angle in degrees.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
An isosceles triangular panel has a 44° angle between its two equal sides. Find both remaining interior angles and the exterior angle beside either base angle.
Why this math matters
A sketch may look symmetric without proving anything. A stated equality of sides supplies the reason that two angles match. Combining that fact with an angle total lets you solve a shape without measuring the drawing with a protractor.
Set up the model
A useful answer starts with clear assumptions:
- The panel is a nondegenerate triangle in a flat Euclidean plane.
- The 44° angle is the vertex angle between the equal sides.
- A base side is extended in a straight line to form the exterior angle.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Find a triangular panel's missing angles
PausedQuestion: Start with the question. Paused.
Question
Start with the question
An isosceles triangular panel has a 44° angle between its two equal sides. Find both remaining interior angles and the exterior angle beside either base angle.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Identify the repeated angle
44° + b + b = 180°
Each base angle is opposite one of the equal sides. They therefore have the same measure, represented by b.
Solve and classify
2b = 136°; b = 68°
Subtract the vertex angle, then divide the remainder equally. All three interior angles are below 90°, making the triangle acute.
Extend the base
exterior angle = 180° − 68° = 112°
The interior and adjacent exterior angles make a straight angle. The exterior angle also equals 44° + 68°, the two remote interior angles.
The result
The base angles are 68° each, and either adjacent exterior angle is 112°.
The panel is isosceles by side lengths and acute by angle measures. These descriptions answer different classification questions; neither description alone determines the panel's size.
Common mistakes to catch
- The 44° angle is not one of the repeated base angles.
- A triangle's interior total is 180°, not the 360° total for a simple quadrilateral.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
An isosceles triangle has a 100° vertex angle. Find its base angles.
Show a hint
Split the remaining 80° equally.
Reveal answer and explanation
40° and 40°
100 + 40 + 40 = 180; this is an obtuse isosceles triangle.
Practice 2
A plane triangle has angles 52° and 61°. Find the third angle.
Show a hint
Subtract both given angles from 180°.
Reveal answer and explanation
67°
180 − 52 − 61 = 67. No equal-side assumption is needed.
Take the idea with you
Separate what the problem states from what the drawing merely suggests whenever using symmetry or equal lengths.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: How much flooring would a room need?
Completion is your own study record, not a test score. It stays in this browser, does not sync to another device, and can be removed by clearing browser data.