Deductive Geometry (Reasoning) 2
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 3 questions completed
Questions:
- 1
- 2
- 3
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- Answered
- Review
-
Question 1 of 3
1. Question
Find the value of `a`
- `a=` (35)
Hint
Help VideoCorrect
Correct!
Incorrect
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°Supplementary angles are when two angles have a sum of `180°.` Typically, these angles lie on a straight line.To find the value of `a`, first find its supplementary angles and set their sum to `180°`First, note that the two missing interior angles are base angles in an isosceles triangle. Hence, they are equal.Let 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+40` `=` `180` `2x+40` `=` `180` Simplify `2x+40` `-40` `=` `180` `-40` Subtract `40` from both sides `2x` `=` `140` `2x` `divide2` `=` `140` `divide2` Divide both sides by `2` `x` `=` `70°` Now, let the alternate angle of `40°` be `y`. Since they are alternate angles, they are equal.
Therefore, `/_ y=40°`Finally, we can see from the diagram that the exterior angles `2a`, `y=40°` and the interior angle `x=70°` 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`.`2a+x+y` `=` `180` `2a+70+40` `=` `180` Plug in the known values `2a+110` `=` `180` Simplify `2a+110` `-110` `=` `180` `-110` Subtract `110` from both sides `2a` `=` `70` `2a` `divide2` `=` `70` `divide2` Divide both sides by `2` `a` `=` `35°` `/_ a=35°` -
Question 2 of 3
2. Question
If the triangle is equally divided in half by `MQ`, find the value of `/_MPQ`
- `/_MPQ=` (39)`°`
Hint
Help VideoCorrect
Keep Going!
Incorrect
An exterior angle of a triangle is equal to the sum of two interior angles opposite of it.To solve for `/_MPQ`, add it to the value of `/_PQR`, then set their sum to be the exterior angle `145°`First, we can see in the diagram that the interior angles `92°` and `/_MQR` are opposite to the exterior angle `145°`
Since the exterior angles of a triangle is equal to the sum of the two opposite interior angles, add the interior angle measures and set their sum to `145°.` Then, solve for `/_MQR`.`/_MQR+92` `=` `145` `/_MQR+92` `-92` `=` `145` `-92` Subtract `92` from both sides `/_MQR` `=` `53°` Next, we can see from the diagram that line `MQ` divides the triangle equally
Therefore, `/_MQR` and `/_MQP` will also be equal, which is `53°`Finally, we can see in the diagram that the interior angles `/_MPQ` and `/_PQR` are opposite to the exterior angle `145°`
Since the exterior angles of a triangle is equal to the sum of the two opposite interior angles, add the interior angle measures and set their sum to `145°.` Then, solve for `/_MPQ`.`/_PQR=/_MQR+/_MQP``/_MPQ+/_PQR` `=` `145` `/_MPQ+(53+53)` `=` `145` Plug in the known values `/_MPQ+106` `=` `145` Simplify `/_MPQ+106` `-106` `=` `145` `-106` Subtract `106` from both sides `/_MPQ` `=` `39°` `/_ MPQ=39°` -
Question 3 of 3
3. Question
Find the value of `/_BDC`
- `/_BDC=` (133)`°`
Hint
Help VideoCorrect
Fantastic!
Incorrect
The sum of the interior angles in a triangle is 180°Derive the equation for the interior angles of the larger triangle and use that equation to solve for `/_BDC`First, consider that the interior angles of the larger triangle add to `180°`.
Add the angle measures of this larger triangle and set their sum to `180°.` Then, simplify the equation.`/_ABC+/_ACB+86` `=` `180` `(m+m)+(n+n)+86` `=` `180` Plug in the known values `2m+2n+86` `=` `180` Simplify `2m+2n+86` `-86` `=` `180` `-86` Subtract `86` from both sides `2m+2n` `=` `94` `(2m+2n)``divide2` `=` `94` `divide2` Divide both sides by `2` `m+n` `=` `47°` Now, consider that the interior angles of the smaller triangle add to `180°`.
Add the angle measures of the smaller triangle and set their sum to `180°.` Then, solve for `/_BDC`.Note that `m+n=47°``m+n` `+/_BDC` `=` `180` `47` `+/_BDC` `=` `180` Plug in the known values `47+/_BDC` `-47` `=` `180` `-47` Subtract `47` from both sides `/_BDC` `=` `133°` `/_ BDC=133°`
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