Learn with Amar
Teaching video
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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to build an equation from triangle angles.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Combine like terms and solve a one-step equation.
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
A triangle has angles x°, 2x°, and 30°. Find every angle and classify the triangle by its largest angle.
Why this math matters
The interior angles of a Euclidean triangle total 180°, linking geometry to a linear equation. Translate geometric relationships into equations, then check that the resulting angles form a possible figure.
Set up the model
A useful answer starts with clear assumptions:
- The triangle lies in a Euclidean plane.
- The expressions label its three interior angles.
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.
Build an equation from triangle angles
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A triangle has angles x°, 2x°, and 30°. Find every angle and classify the triangle by its largest 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.
Represent the quantities
x + 2x + 30 = 180
Add all three interior angles using the triangle-angle sum.
Apply the relationship
3x = 150; x = 50
Subtract the known angle and divide the remaining total by three.
Check and interpret
angles: 50°, 100°, 30°; the triangle is obtuse
The angles sum to 180°, and the 100° angle exceeds 90°.
The result
angles: 50°, 100°, 30°; the triangle is obtuse
The angles sum to 180°, and the 100° angle exceeds 90°.
Common mistakes to catch
- An exterior angle is not one of the three interior angles in the 180° sum.
- The value x alone may not be the requested list of angles.
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 vertex angle 40°. Find each base angle.
Show a hint
The remaining two angles are equal.
Reveal answer and explanation
70° each
(180 − 40)/2 = 70.
Practice 2
Can 70°, 60°, and 60° be the interior angles of a planar triangle?
Show a hint
Add all three angles.
Reveal answer and explanation
No
Their sum is 190°, which violates the Euclidean triangle-angle sum.
Take the idea with you
Translate geometric relationships into equations, then check that the resulting angles form a possible figure.
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: Distinguish supplementary and vertical angles
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