Simplifying and Combining Like Terms: Using additional geometric shapes

Combining like terms One sided equations Opening parentheses Solving an equation with fractions Exercises with fractions Solving an equation using all techniques Equations with variables on both sides

Question 1

Look at triangle ABC below.

$\( ∢A+∢B=2∢C \)$

$\( ∢B=3∢A \)$

Calculate the size of angle $\sphericalangle C\text{.}$

Question 2

$\( ∢B \)$ is 2 times bigger than $\( ∢A \)$ and $\( ∢C \)$ is 3 times bigger than $\( ∢B \)$ .

Calculate $\( ∢A \)$ .

Question 3

The triangle ABC is shown below.

angle $\( ∢A=70° \)$ .

$\frac{∢B}{∢C}=\frac{1}{3}$

Calculate angle $\( ∢C \)$ .

Question 4

The triangle ABC is shown below.

$\( ∢C=2∢B \)$

$\( ∢B=5∢A \)$

Calculate $\( ∢C \)$ $\( \)$ .

Question 5

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?

Examples with solutions for Simplifying and Combining Like Terms: Using additional geometric shapes

Exercise #1

Look at triangle ABC below.

$∢A+∢B=2∢C$

$∢B=3∢A$

Calculate the size of angle $\sphericalangle C\text{.}$

Video Solution

Answer

60°

Exercise #2

$∢B$ is 2 times bigger than $∢A$ and $∢C$ is 3 times bigger than $∢B$ .

Calculate $∢A$ .

Video Solution

Answer

20°

Exercise #3

The triangle ABC is shown below.

angle $∢A=70°$ .

$\frac{∢B}{∢C}=\frac{1}{3}$

Calculate angle $∢C$ .

Video Solution

Answer

82.5°

Exercise #4

The triangle ABC is shown below.

$∢C=2∢B$

$∢B=5∢A$

Calculate $∢C$ .

Video Solution

Answer

$56\frac{1}{4}°$

Exercise #5

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?

Video Solution

Answer

Yes, 40°.