730 Chapter 9 An Introduction to Geometry
Since the angles are congruent, their measures are equal.
To eliminate 6xfrom the right side, subtract 6xfrom both
sides.
To isolate the variable term 3x, undo the subtraction of
15° by adding 15° to both sides: 30°15°45°.
To isolate x, undo the multiplication by 3 by dividing both
sides by 3.
Thus, is 15°.xx15°3 x45°3 x15°30°9 x15° 6 x30°EXAMPLE (^5) In the figure,.
a.Find.
b.Find the measures of both angles labeled in the
figure.
StrategyWe will use the interior angles property
to write an equation that mathematically models the
situation.
WHYWe can then solve the equation to find.
Solution
a.Because the angles are interior angles on the same side of the transversal, they
are supplementary.
The sum of the measures of two supplementary
angles is 180°.
Combine like terms: 3x 3 x 6 x.
To undo the subtraction of 60°, add 60° to both
sides: 180°60°240°.
To isolate x,undo the multiplication by 6 by
dividing both sides by 6.
Thus, is 40°.
This problem may be solved using a different approach. In the figure
below, we see that and the angle with measure are corresponding
angles.
Because and are parallel, all pairs of corresponding angles are
congruent. Therefore,
m(1) 3 x80°
l 1 l 2
1 3 x80°
x
x40°
6 x240°
6 x60°180°
3 x80° 3 x20°180°
x
x
l 1 l 2
Self Check 5
In the figure below,.
a.Find.
b.Find the measures of both
angles labeled in the figure.
x
l 1 l 2
3 x + 20 °
l^3 x^ −^80 °
2
l 1
3 x + 20 °
l^3 x^ −^80 °
2
l 1 1
In the figure, we also see that and the angle with measure are
supplementary. That means that the sum of their measures must be 180°. We
have
Replace m(1) with 3x80°.
This is the same equation that we obtained in the previous solution. When it is
solved, we find that is 40°.x
3 x80° 3 x20°180°
m(1) 3 x20°180°
1 3 x20°
Now TryProblem 29
x + 40°
2 x + 50°
l 1
l 2