Triangle Geometry 2

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Year 8

Geometry

Triangle Geometry

Triangle Geometry 2

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Question 1 of 4

Find the value of

x

$x$

$x =$ $x=$ (55)°

Incorrect

The sum of the interior angles in a triangle is $180 °$ $180°$

Since the interior angles of a triangle add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for

x

$x$ .

$x + 75 + 50$ $x+75+50$	$=$ $=$	$180$ $180$
$x + 125$ $x+125$	$=$ $=$	$180$ $180$	Simplify
$x + 125$ $x+125$ $- 125$ $-125$	$=$ $=$	$180$ $180$ $- 125$ $-125$	Subtract $125$ $125$ from both sides
$x$ $x$	$=$ $=$	$55 °$ $55°$

∠ x = 55 °

$/_ x=55°$

Question 2 of 4

Find the value of

a

$a$

$a =$ $a=$ (20)

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The sum of the interior angles in a triangle is $180 °$ $180°$

Since the interior angles of a triangle add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for

a

$a$ .

$3 a + a + 30 + 70$ $3a+a+30+70$	$=$ $=$	$180$ $180$
$4 a + 100$ $4a+100$	$=$ $=$	$180$ $180$	Simplify
$4 a + 100$ $4a+100$ $- 100$ $-100$	$=$ $=$	$180$ $180$ $- 100$ $-100$	Subtract $100$ $100$ from both sides
$4 a$ $4a$	$=$ $=$	$80$ $80$
$4 a$ $4a$ $\div 4$ $divide4$	$=$ $=$	$80$ $80$ $\div 4$ $divide4$	Divide both sides by $4$ $4$
$a$ $a$	$=$ $=$	$20$ $20$

a = 20

$a=20$

Question 3 of 4

3. Question
Find the value of $a$ $a$
- $a =$ $a=$ (120)°
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An exterior angle of a triangle is equal to the sum of two interior angles opposite of it.

To solve for $a$ $a$ , add the two given interior angles.

We can see in the diagram that the interior angles $68 °$ $68°$ and $52 °$ $52°$ are opposite to the exterior angle $a$ $a$

Therefore, $a$ $a$ will be equal to the sum of the two interior angles opposite of it.

$a$ $a$ $=$ $=$ $68 + 52$ $68+52$

$a$ $a$ $=$ $=$ $120 °$ $120°$

$∠ a = 120 °$ $/_ a=120°$

Question 4 of 4

Find the value of

b

$b$

$b =$ $b=$ (89)°

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Supplementary angles are when two angles have a sum of

180 ° .

$180°.$ Typically, these angles lie on a straight line.

The sum of the interior angles in a triangle is $180 °$ $180°$

To solve for

b

$b$ , solve for its supplementary angle by adding the given interior angles and setting their sum to

180 °

$180°$

Let this supplementary angle be

a

$a$ .

First, we can see from the diagram that the exterior angle

125 °

$125°$ and the interior angle

a

$a$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for the value of

a

$a$ .

$a + 125$ $a+125$	$=$ $=$	$180$ $180$
$a + 125$ $a+125$ $- 125$ $-125$	$=$ $=$	$180$ $180$ $- 125$ $-125$	Subtract $125$ $125$ from both sides
$a$ $a$	$=$ $=$	$55 °$ $55°$

Finally, since the interior angles of a triangle add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for

b

$b$ .

$a + b + 36$ $a+b+36$	$=$ $=$	$180$ $180$
$55 + b + 36$ $55+b+36$	$=$ $=$	$180$ $180$	Plug in the known values
$b + 91$ $b+91$	$=$ $=$	$180$ $180$	Simplify
$b + 91$ $b+91$ $- 91$ $-91$	$=$ $=$	$180$ $180$ $- 91$ $-91$	Subtract $91$ $91$ from both sides
$b$ $b$	$=$ $=$	$89 °$ $89°$

∠ b = 89 °

$/_ b=89°$

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Quiz summary

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1. Question

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2. Question

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Well Done!

3. Question

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4. Question

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Quizzes

$a$ $a$	$=$ $=$	$68 + 52$ $68+52$
$a$ $a$	$=$ $=$	$120 °$ $120°$