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

Exercise #1

Look at the triangle below.

Calculate the size of angle α \alpha .

AAABBBCCC40α63

Video Solution

Answer

103

Exercise #2

AB || CD

x = 80

Calculate the size of the α \alpha .

AAABBBCCCDDDxα70β

Video Solution

Answer

30

Exercise #3

AB||CD

x = 50

Calculate the size of angle α \alpha .

AAABBBCCCDDDx63αβ

Video Solution

Answer

67

Exercise #4

ΔABC is a scalene triangle with acute angles.


Which angle is larger,
C ∢C or A ∢A ?

AAABBBCCC

Video Solution

Answer

There is no way to know.

Exercise #5

ABC is an isosceles triangle

(A ∢A is the predominant angle).

Which angle is larger,B ∢B orC ∢C ?

AAACCCBBB

Video Solution

Answer

C=B ∢C=∢B

Exercise #6

Triangle ABC is an obtuse triangle.

Which angle is larger, B ∢B or A ∢A ?

AAABBBCCC

Video Solution

Answer

∢B>∢A

Exercise #7

ABC is an equilateral triangle.

Which angle is larger, B ∢B orA ∢A ?

AAABBBCCC

Video Solution

Answer

A=B ∢A=∢B

Exercise #8

The triangle ABC is a right triangle.

Which angle is larger, B ∢B or A ∢A ?

AAABBBCCC

Video Solution

Answer

∢A>∢B

Exercise #9

AB || CD

Calculate the size of the angle α \alpha .

AAABBBCCCDDDxα77β120

Video Solution

Answer

43

Exercise #10

AB || CD

Calculate the size of angle α \alpha .

AAABBBCCCDDDx47αβ131

Video Solution

Answer

84

Exercise #11

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 #12

The triangle ABC is right angled.

A=4B ∢A=4∢B

Calculate angles B ∢B and A ∢A .

AAABBBCCC

Video Solution

Answer

72 , 18

Exercise #13

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 #14

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°

Exercise #15

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 #16

ABC is an obtuse triangle.

C=12A ∢C=\frac{1}{2}∢A

B=3A ∢B=3∢A

Is it possible to calculate A ∢A ?

If so, then what is it?

AAABBBCCC

Video Solution

Answer

Yes, 40°.

Exercise #17

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