Triangle Geometry 1

Years

Year 8

Geometry

Triangle Geometry

Triangle Geometry 1

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Question 1 of 5

Find the value of

x

$x$

$x =$ $x=$ (68)°

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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

x

$x$ .

$x + 25 + 87$ $x+25+87$	$=$ $=$	$180$ $180$
$x + 112$ $x+112$	$=$ $=$	$180$ $180$	Simplify
$x + 112$ $x+112$ $- 112$ $-112$	$=$ $=$	$180$ $180$ $- 112$ $-112$	Subtract $112$ $112$ from both sides
$x$ $x$	$=$ $=$	$68 °$ $68°$

∠ x = 68 °

$/_ x=68°$

Question 2 of 5

2. Question
Find the value of $x$ $x$
- $x =$ $x=$ (60)°
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The sum of the interior angles in a triangle is $180 °$ $180°$

We can see in the image that the triangle is an equilateral triangle, which means it has equal sides.

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 $x$ $x$ .

$x + x + x$ $x+x+x$ $=$ $=$ $180$ $180$

$3 x$ $3x$ $=$ $=$ $180$ $180$ Simplify

$3 x$ $3x$ $\div 3$ $divide3$ $=$ $=$ $180$ $180$ $\div 3$ $divide3$ Divide both sides by $3$ $3$

$x$ $x$ $=$ $=$ $60 °$ $60°$

$∠ x = 60 °$ $/_ x=60°$

Question 3 of 5

Find the value of

x

$x$

$x =$ $x=$ (45)°

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

$x$ .

$x + 71 + 64$ $x+71+64$	$=$ $=$	$180$ $180$
$x + 135$ $x+135$	$=$ $=$	$180$ $180$	Simplify
$x + 135$ $x+135$ $- 135$ $-135$	$=$ $=$	$180$ $180$ $- 135$ $-135$	Subtract $135$ $135$ from both sides
$x$ $x$	$=$ $=$	$45 °$ $45°$

∠ x = 45 °

$/_ x=45°$

Question 4 of 5

Find the value of

x

$x$

$x =$ $x=$ (25)°

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

$x$ .

$x + 20 + 135$ $x+20+135$	$=$ $=$	$180$ $180$
$x + 155$ $x+155$	$=$ $=$	$180$ $180$	Simplify
$x + 155$ $x+155$ $- 155$ $-155$	$=$ $=$	$180$ $180$ $- 155$ $-155$	Subtract $155$ $155$ from both sides
$x$ $x$	$=$ $=$	$25 °$ $25°$

∠ x = 25 °

$/_ x=25°$

Question 5 of 5

Find the value of

x

$x$ and

y

$y$

$x =$ $x=$ (75) $°$ $°$

$y =$ $y=$ (30) $°$ $°$

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An Isosceles Triangle has two congruent sides (the two sides with dashes) and the two base angles are equal.

To solve for

y

$y$ , add it to

x

$x$ and

75 °

$75°$ , then set their sum to

180 °

$180°$ .

Since the base angles in an isosceles triangle are equal, $x$ $x$ is equal to

75 °

$75°$

x

$x$

=

$=$

75

$75$

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 $y$ $y$ .

$y$ $y$ $+ 75 + 75$ $+75+75$	$=$ $=$	$180$ $180$
$y$ $y$ $+ 150$ $+150$	$=$ $=$	$180$ $180$	Simplify
$y$ $y$ $+ 150$ $+150$ $- 150$ $-150$	$=$ $=$	$180$ $180$ $- 150$ $-150$	Subtract $150$ $150$ from both sides
$y$ $y$	$=$ $=$	$30 °$ $30°$

∠ x = 75 °

$/_ x=75°$

∠ y = 30 °

$/_ y=30°$

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Quiz summary

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1. Question

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2. Question

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Quizzes

$x + x + x$ $x+x+x$	$=$ $=$	$180$ $180$
$3 x$ $3x$	$=$ $=$	$180$ $180$	Simplify
$3 x$ $3x$ $\div 3$ $divide3$	$=$ $=$	$180$ $180$ $\div 3$ $divide3$	Divide both sides by $3$ $3$
$x$ $x$	$=$ $=$	$60 °$ $60°$