Deductive Geometry (Reasoning) 2

Years

Year 10

Geometry

Deductive Geometry (Reasoning)

Deductive Geometry (Reasoning) 2

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 3

Find the value of

$a$

$a=$ (35)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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

If the triangle is equally divided in half by

$MQ$ , find the value of

$/_MPQ$

$/_MPQ=$ (39) $°$

Question 3 of 3

Find the value of

$/_BDC$

$/_BDC=$ (133) $°$

$/_MQR+92$	$=$	$145$
$/_MQR+92$ $-92$	$=$	$145$ $-92$	Subtract $92$ from both sides
$/_MQR$	$=$	$53°$

$/_MPQ+/_PQR$	$=$	$145$
$/_MPQ+(53+53)$	$=$	$145$	Plug in the known values
$/_MPQ+106$	$=$	$145$	Simplify
$/_MPQ+106$ $-106$	$=$	$145$ $-106$	Subtract $106$ from both sides
$/_MPQ$	$=$	$39°$

Deductive Geometry (Reasoning) 2

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Correct!

2. Question

Hint

Keep Going!

3. Question

Hint

Fantastic!

Quizzes

$/_ABC+/_ACB+86$	$=$	$180$
$(m+m)+(n+n)+86$	$=$	$180$	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 $2$
$m+n$	$=$	$47°$

$m+n$ $+/_BDC$	$=$	$180$
$47$ $+/_BDC$	$=$	$180$	Plug in the known values
$47+/_BDC$ $-47$	$=$	$180$ $-47$	Subtract $47$ from both sides
$/_BDC$	$=$	$133°$