Transcript Find the measure of angle x.

Brainstorm
• What are different ways we can find the
missing angles of a triangle or intersecting
lines?
Complementary angles = 90°
Supplementary angles = 180°
Vertical angles are equal to each other
Alternate interior and exterior angles of parallel lines are equal
Definition
• Quadrilateral – a polygon
with 4 angles and 4 straight
sides. All the angles add
together to equal 360º
90º
90º
90º
90º
Finding the Fourth Angle of a Quadrilateral
The sum of the interior angles of a
quadrilateral are equal to 360°. To find the
fourth angle of a quadrilateral when the other
three angles are known, subtract the number
of degrees in the other three angles from
360°.
Example: How many degrees are in the fourth
angle of a quadrilateral whose other three
angles are 80° and 110° and 95°? Answer: 360°
- 80° - 110° - 95° = 75°
What is the missing
angle?
90º
90º
90º
?
90º
90º
90º
+ ?
360º
Finding Missing Angle Measures
of Quadrilaterals
Opposite angles of parallelograms are equal.
If you divide a parallelogram into two triangles they are
congruent, so their angles also have to be congruent.
Remember parallel lines cut by a transversal?
Brainstorm with the person next to you: What do you
think I can prove if I divide this parallelogram in half
from the 65° to the y?
Finding Missing Angle Measures
of Quadrilaterals
Two ways to solve:
1. Using rules about opposite
angles of parallelograms.
2. Using algebra and rules about
angle measures of quadrilaterals.
There is also a theorem in geometry that tells us that in all
quadrilaterals, the sum of the measures of the angles is
360o. This can be used in many situations, including problems
where you need to find the measures of angles.
1
. Problem: Find the measure of angle x.
Find the missing angle measures:
Draw the figure first.
88°
79°