Card 1 of 20
EasyStudy card 1
Prompt
What is the sum of a triangle's interior angles?
Answer
\(180^\circ\).
MathChapter 17: Triangles
Flashcards
Angles of a Triangle Flashcards
Twenty cards on triangle sums, exterior angles, isosceles relationships, and theorem conditions.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
State the Exterior Angle Theorem.
Answer
An exterior angle equals the sum of the two remote interior angles.
Card 3 of 20
EasyStudy card 3
Prompt
What is the relationship between an exterior angle and its adjacent interior angle?
Answer
They are supplementary and total \(180^\circ\).
Card 4 of 20
EasyStudy card 4
Prompt
If two sides of a triangle are congruent, what follows?
Answer
Their opposite angles are congruent.
Card 5 of 20
EasyStudy card 5
Prompt
State the converse of the Isosceles Triangle Theorem.
Answer
If two angles are congruent, their opposite sides are congruent.
Card 6 of 20
EasyStudy card 6
Prompt
What are remote interior angles?
Answer
The two triangle angles not adjacent to the chosen exterior angle.
Card 7 of 20
EasyStudy card 7
Prompt
What do matching side ticks mean?
Answer
The marked sides are congruent.
Card 8 of 20
MediumStudy card 8
Prompt
A triangle has angles 48° and 77°. Find the third.
Answer
55°.
Card 9 of 20
MediumStudy card 9
Prompt
Remote angles are 36° and 69°. Find the exterior angle.
Answer
105°.
Card 10 of 20
MediumStudy card 10
Prompt
An exterior angle is 124°. Find its adjacent interior angle.
Answer
56°.
Card 11 of 20
MediumStudy card 11
Prompt
An isosceles triangle has vertex angle 70°. Find either base angle.
Answer
55°.
Card 12 of 20
MediumStudy card 12
Prompt
If AB = AC, which angles are equal?
Answer
\(\angle B=\angle C\), the angles opposite those sides.
Card 13 of 20
MediumStudy card 13
Prompt
What does a vertex-angle bisector do in an isosceles triangle?
Answer
It is perpendicular to the base and bisects the base.
Card 14 of 20
MediumStudy card 14
Prompt
Can every triangle angle bisector be assumed perpendicular to the opposite side?
Answer
No; that conclusion needs the isosceles vertex-bisector conditions.
Card 15 of 20
MediumStudy card 15
Prompt
What sum do the acute angles of a right triangle have?
Answer
\(90^\circ\).
Card 16 of 20
MediumStudy card 16
Prompt
Why can an interior triangle angle not be 180°?
Answer
The other two angles must also be positive, while all three total 180°.
Card 17 of 20
HardStudy card 17
Prompt
What is the fastest exterior-angle check?
Answer
Verify exterior plus adjacent interior is 180° and exterior equals the two remotes.
Card 18 of 20
HardStudy card 18
Prompt
A triangle only looks isosceles. May you set base angles equal?
Answer
No; a statement or congruence marks are required.
Card 19 of 20
HardStudy card 19
Prompt
In an algebraic triangle problem, when should x be substituted back?
Answer
Whenever the question asks for an angle rather than for x.
Card 20 of 20
HardStudy card 20
Prompt
Name four common triangle-angle reasons.
Answer
Angle sum, exterior-angle theorem, straight-angle supplement, and isosceles correspondence.
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