Triangle Geometry 3
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Question 1 of 4
1. Question
Find the value of `a`
- `a=` (40)°
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Supplementary angles are when two angles have a sum of `180°.` Typically, these angles lie on a straight line.
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 solve for `a`, find the measure of the missing interior angles, add it to `a` and set their sum to `180°`.First, we can see from the diagram that the exterior angle `110°` and the interior angle `b` 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 `a`.`b+110` `=` `180` `b+110` `-110` `=` `180` `-110` Subtract `110` from both sides `b` `=` `70°` Next, since the base angles in an isosceles triangle are equal, `c` is equal to `70˚``c` `=` `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 `b`.`a+b+c` `=` `180` `a+70+70` `=` `180` Plug in the known values `a+140` `=` `180` Simplify `a+140` `-140` `=` `180` `-140` Subtract `140` from both sides `a` `=` `40°` `/_ a=40°` -
Question 2 of 4
2. Question
Find the value of `x`
- `x=` (150)°
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Well Done!
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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 solve for `x`, find the supplementary angle of `z`.First, we can see from the diagram that the exterior angle `100°` and the interior angle `y` 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 `y`.`y+100` `=` `180` `y+100` `-100` `=` `180` `-100` Subtract `100` from both sides `y` `=` `80°` Next, since the interior angles of a triangle add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for `z`.`y+z+80` `=` `180` `80+z+70` `=` `180` Plug in the known values `z+150` `=` `180` Simplify `z+150` `-150` `=` `180` `-150` Subtract `150` from both sides `z` `=` `30°` Finally, we can see from the diagram that the exterior angle `x` and the interior angle `z` 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+z` `=` `180` `x+30` `=` `180` Plug in the known values `x+30` `-30` `=` `180` `-30` Subtract `30` from both sides `x` `=` `150°` `/_ x=150°` -
Question 3 of 4
3. Question
Find the value of `x`
- `x=` (132)°
Correct
Excellent!
Incorrect
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 solve for `x`, find the supplementary angle of `z`First, we can see from the diagram that the exterior angle `88°` and the interior angle `y` 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 `y`.`y+88` `=` `180` `y+88` `-88` `=` `180` `-88` Subtract `88` from both sides `y` `=` `92°` Next, since the interior angles of a triangle add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for `z`.`y+z+40` `=` `180` `92+z+40` `=` `180` Plug in the known values `z+132` `=` `180` Simplify `z+132` `-132` `=` `180` `-132` Subtract `132` from both sides `z` `=` `48°` Finally, we can see from the diagram that the exterior angle `x` and the interior angle `z` 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+z` `=` `180` `x+48` `=` `180` Plug in the known values `x+48` `-48` `=` `180` `-48` Subtract `48` from both sides `x` `=` `132°` `/_ x=132°` -
Question 4 of 4
4. Question
Find the value of `a`
- `a=` (154)°
Correct
Keep Going!
Incorrect
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 solve for `a`, find the supplementary angle of `z`.First, we can see from the diagram that the exterior angle `122°` 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+122` `=` `180` `x+122` `-122` `=` `180` `-122` Subtract `122` from both sides `x` `=` `58°` Next, we can see from the diagram that the exterior angle `84°` and the interior angle `y` 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 `y`.`y+84` `=` `180` `y+84` `-84` `=` `180` `-84` Subtract `84` from both sides `y` `=` `96°` Now, since the interior angles of a triangle add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for `z`.`x+y+z` `=` `180` `58+96+z` `=` `180` Plug in the known values `z+154` `=` `180` Simplify `z+154` `-154` `=` `180` `-154` Subtract `154` from both sides `z` `=` `26°` Finally, we can see from the diagram that the exterior angle `a` and the interior angle `z` 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 `a`.`a+z` `=` `180` `a+26` `=` `180` Plug in the known values `a+26` `-26` `=` `180` `-26` Subtract `26` from both sides `a` `=` `154°` `/_ a=154°`
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