Deductive Geometry (Reasoning) 1
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Question 1 of 4
1. Question
Find the value of `x`
- `x=` (60)`°`
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The sum of the interior angles in a triangle is 180°Find the value of the angle alternate to `x`. Let this angle be `y`.First, since the interior angles of a triangle add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for `y`.Note that the angle marked with a square is a right angle, which is equal to `90°.``y+90+30` `=` `180` `y+120` `=` `180` Simplify `y+120` `-120` `=` `180` `-120` Subtract `120` from both sides `y` `=` `60°` Finally, we can see from the diagram that `y` and `x` are alternate angles, which means they are equal
Therefore, `/_ x=60°``/_ x=60°` -
Question 2 of 4
2. Question
Find the value of `a`
- `a=` (73)`°`
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Supplementary angles are when two angles have a sum of `180°.` Typically, these angles lie on a straight line.The sum of the interior angles in a triangle is 180°Find the two missing interior angles in the triangle then solve for `a` by equating them to `180°`Let the first missing interior angle be `b`.
We can see from the diagram that `40°` and `b` are alternate angles, which means they are equal
Therefore, `/_ b=40°`Next, let the second missing interior angle be `c`.
We can see from the diagram that the exterior angle `113°` and the interior angle `c` lie on a straight line. Therefore, they are supplementary angles
Since supplementary angles add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for the value of `c`.`c+113` `=` `180` `c+113` `-113` `=` `180` `-113` Subtract `113` from both sides `c` `=` `67°` Finally, since the interior angles of a triangle add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for `a`.`a+b+c` `=` `180` `a+40+67` `=` `180` Plug in the known values `a+107` `=` `180` Simplify `a+107` `-107` `=` `180` `-107` Subtract `107` from both sides `a` `=` `73°` `/_ a=73°` -
Question 3 of 4
3. Question
Find the value of `a` and `b`
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`a=` (110)`°``b=` (35)`°`
Hint
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An Isosceles Triangle has two congruent sides (the two sides with dashes) and the two base angles are equal.The sum of the interior angles in a triangle is 180°To find the value of `b`, first find the value of `/_KML`To find the value of `a`, first find the two missing interior angles in the triangle then solve for `a` by equating them to `180°`First, since the base angles in an isosceles triangle are equal, `/_MKL` and `/_KML` are equalLet their value be `x`
Next, since the interior angles of a triangle add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for `x`.`x+x+110` `=` `180` `2x+110` `=` `180` Simplify `2x+110` `-110` `=` `180` `-110` Subtract `110` from both sides `2x` `=` `70` `2x` `divide2` `=` `70` `divide2` Divide both sides by `2` `x` `=` `35°` Next, we can see from the diagram that `110°` and `35°+b` are co-interior angles, which add up to `180°`
Since co-interior angles add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for the value of `b`.`b+x+110` `=` `180` `b+35+110` `=` `180` Plug in the known values `b+145` `=` `180` Simplify `b+145` `-145` `=` `180` `-145` Subtract `145` from both sides `b` `=` `35°` Now, since the base angles in an isosceles triangle are equal, `/_KJM` is also equal to `35˚``/_KJM` `=` `35` 
Finally, since the interior angles of a triangle add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for `a`.`a+b+/_KJM` `=` `180` `a+35+35` `=` `180` Plug in the known values `a+70` `=` `180` Simplify `a+70` `-70` `=` `180` `-70` Subtract `70` from both sides `a` `=` `110°` `/_ a=110°``/_ b=35°` -
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Question 4 of 4
4. Question
Find the value of `x`, `y` and `z`
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`x=` (70)`°``y=` (70)`°``z=` (40)`°`
Hint
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Supplementary angles are when two angles have a sum of `180°.` Typically, these angles lie on a straight line.The sum of the interior angles in a triangle is 180°To find the value of `y`, first find its alternate angleTo find the value of `x`, first find its supplementary angle and set their sum to `180°`To find the value of `z`, first find the two missing interior angles in the triangle then solve for `z` by equating them to `180°`First, we can see from the diagram that `70°` and `y` are alternate angles, which means they are equal
Therefore, `y=70°`Next, we can see from the diagram that the exterior angle `110°` and the interior angle `x` lie on a straight line. Therefore, they are supplementary angles
Since supplementary angles add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for the value of `x`.`x+110` `=` `180` `x+110` `-110` `=` `180` `-110` Subtract `110` from both sides `x` `=` `70°` Finally, since the interior angles of a triangle add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for `z`.`z+x+y` `=` `180` `z+70+70` `=` `180` Plug in the known values `z+140` `=` `180` Simplify `z+140` `-140` `=` `180` `-140` Subtract `140` from both sides `z` `=` `40°` `/_ x=70°``/_ y=70°``/_ z=40°` -
Quizzes
- Complementary and Supplementary Angles 1
- Complementary and Supplementary Angles 2
- Complementary and Supplementary Angles 3
- Vertical, Revolution and Reflex Angles 1
- Vertical, Revolution and Reflex Angles 2
- Alternate, Corresponding and Co-Interior Angles 1
- Alternate, Corresponding and Co-Interior Angles 2
- Alternate, Corresponding and Co-Interior Angles 3
- Angles and Parallel Lines
- Triangle Geometry 1
- Triangle Geometry 2
- Triangle Geometry 3
- Quadrilateral Geometry 1
- Quadrilateral Geometry 2
- Congruent Triangles 1
- Congruent Triangles 2
- Deductive Geometry (Reasoning) 1
- Deductive Geometry (Reasoning) 2