Parts of a Triangle: Using angles in a triangle

Calculate Angles in QuadrilateralsClassify a triangle by its sidesDetermine the size of the given anglesFinding the size of angles in a triangleIdentifying and defining elementsIdentifying sides in a triangleIdentifying the sides in a triangle using median and heightIdentify the greater valueIs it possible...?Median in an isosceles triangle - propertiesMedian in a right-angled triangleTrue / falseUsing parallel linesUsing properties of the medianUsing the median to calculate the perimeterUsing the theorem: The median of a triangle divides it into two triangles of the same area
Question 1

ABC is an obtuse triangle.

\( ∢C=\frac{1}{2}∢A \)\( \)

\( ∢B=3∢A \)

Is it possible to calculate \( ∢A \)?

If so, then what is it?

AAABBBCCC

Question 2

AB||CD

x = 50

Calculate the size of angle \( \alpha \).

AAABBBCCCDDDx63αβ

Question 3

AB || CD

x = 80

Calculate the size of the \( \alpha \).

AAABBBCCCDDDxα70β

Question 4

Look at the triangle below.

Calculate the size of angle \( \alpha \).

AAABBBCCC40α63

Question 5

AB || CD

Calculate the size of the angle \( \alpha \).

AAABBBCCCDDDxα77β120

Examples with solutions for Parts of a Triangle: Using angles in a triangle

Exercise #1

ABC is an obtuse triangle.

∢C=12∢A ∢C=\frac{1}{2}∢A

∢B=3∢A ∢B=3∢A

Is it possible to calculate ∢A ∢A ?

If so, then what is it?

AAABBBCCC

Video Solution

Step-by-Step Solution

To solve for ∠A \angle A in triangle △ABC \triangle ABC , we proceed as follows:

  • First, note that the sum of angles in any triangle is 180∘ 180^\circ . Therefore, ∠A+∠B+∠C=180∘ \angle A + \angle B + \angle C = 180^\circ .
  • We know that ∠B=3∠A \angle B = 3 \angle A and ∠C=12∠A \angle C = \frac{1}{2} \angle A .
  • Substitute these expressions into the triangle sum equation: ∠A+3∠A+12∠A=180∘ \angle A + 3\angle A + \frac{1}{2}\angle A = 180^\circ .
  • Combine like terms: ∠A+3∠A+12∠A=4∠A+12∠A=92∠A \angle A + 3\angle A + \frac{1}{2}\angle A = 4\angle A + \frac{1}{2}\angle A = \frac{9}{2}\angle A .
  • The equation becomes 92∠A=180∘ \frac{9}{2} \angle A = 180^\circ .
  • To solve for ∠A \angle A , multiply both sides by 29 \frac{2}{9} :
    • ∠A=29×180∘=40∘\angle A = \frac{2}{9} \times 180^\circ = 40^\circ.
  • Check consistency: ∠A=40∘ \angle A = 40^\circ leads to ∠B=120∘ \angle B = 120^\circ and ∠C=20∘ \angle C = 20^\circ .
  • Verify that △ABC\triangle ABC is consistent with being obtuse: Indeed, the triangle has ∠B=120∘\angle B = 120^\circ which is greater than 90∘90^\circ, confirming the triangle is obtuse.

Therefore, it is possible to calculate ∠A \angle A , and the solution is ∠A=40∘\angle A = 40^\circ.

Answer

Yes, 40°.

Exercise #2

AB||CD

x = 50

Calculate the size of angle α \alpha .

AAABBBCCCDDDx63αβ

Video Solution

Answer

67

Exercise #3

AB || CD

x = 80

Calculate the size of the α \alpha .

AAABBBCCCDDDxα70β

Video Solution

Answer

30

Exercise #4

Look at the triangle below.

Calculate the size of angle α \alpha .

AAABBBCCC40α63

Video Solution

Answer

103

Exercise #5

AB || CD

Calculate the size of the angle α \alpha .

AAABBBCCCDDDxα77β120

Video Solution

Answer

43

Question 1

AB || CD

Calculate the size of angle \( \alpha \).

AAABBBCCCDDDx47αβ131

Question 2

Shown below is the triangle ABC.

\( ∢A \) is 3 times greater than the sum of the rest of the angles.

Calculate \( ∢A \).AAABBBCCC

Question 3

The triangle ABC is right angled.

\( ∢A=4∢B \)

Calculate angles \( ∢B \) and \( ∢A \).

AAABBBCCC

Question 4

Given the triangle ABC.

Dado \( ∢B>90° \) , \( ∢A=20° \)

Is it possible to calculate a ? \( ∢B \)?

If so, find how much the angle is equal to.

\( \)AAABBBCCC20°

Question 5

The triangle ABC is isosceles.

\( ∢C=50° \)

Is it possible to calculate the size of angle \( ∢A \)?

If so, then what is it?

AAABBBCCC50°

Exercise #6

AB || CD

Calculate the size of angle α \alpha .

AAABBBCCCDDDx47αβ131

Video Solution

Answer

84

Exercise #7

Shown below is the triangle ABC.

∢A ∢A is 3 times greater than the sum of the rest of the angles.

Calculate ∢A ∢A .AAABBBCCC

Video Solution

Answer

135°

Exercise #8

The triangle ABC is right angled.

∢A=4∢B ∢A=4∢B

Calculate angles ∢B ∢B and ∢A ∢A .

AAABBBCCC

Video Solution

Answer

72 , 18

Exercise #9

Given the triangle ABC.

Dado ∢B>90° , ∢A=20° ∢A=20°

Is it possible to calculate a ? ∢B ∢B ?

If so, find how much the angle is equal to.

AAABBBCCC20°

Video Solution

Answer

No

Exercise #10

The triangle ABC is isosceles.

∢C=50° ∢C=50°

Is it possible to calculate the size of angle ∢A ∢A ?

If so, then what is it?

AAABBBCCC50°

Video Solution

Answer

Yes, 80°

Question 1

ABC is a right triangle.

\( ∢A=20° \)

Is it possible to calculate the size of \( ∢C \)?

If so, what is it?

AAACCCBBB20°

Question 2

ABC is an isosceles triangle.

DE is parallel to BC.

Angle A is equal to 3X plus 22.

Express the size of angle DEC.

AAABBBCCCDDDEEE

Exercise #11

ABC is a right triangle.

∢A=20° ∢A=20°

Is it possible to calculate the size of ∢C ∢C ?

If so, what is it?

AAACCCBBB20°

Video Solution

Answer

Yes, 70°.

Exercise #12

ABC is an isosceles triangle.

DE is parallel to BC.

Angle A is equal to 3X plus 22.

Express the size of angle DEC.

AAABBBCCCDDDEEE

Video Solution

Answer

101+1.5x 101+1.5x