ACT Math : Acute / Obtuse Triangles
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Example Questions
Example Question #164 :Plane Geometry
Two interior angles in an obtuse triangle measure
Interior angles of a triangle always add up to 180 degrees.
Example Question #165 :Plane Geometry
In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?
Since the sum of the angles of a triangle is
If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.
Example Question #166 :Plane Geometry
In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?
A (Angle A = 41°)
B C
82
98
41
90
98
如果是41°角,角必须41°C,since AB=BC. So, the sum of these 2 angles is:
41° + 41° = 82°
Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:
180° - 82° = 98°
Example Question #171 :Plane Geometry
Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.
70°
80°
60°
50°
50°
To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.
Example Question #2 :How To Find An Angle In An Acute / Obtuse Triangle
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is
Find the measure of
The measure of
Because the measures of the three angles in a triangle must add up to
Example Question #172 :Plane Geometry
Observe the following image and answer the question below:
Are triangles
Not enough information to decide.
Maybe
No
Yes
Yes
Two triangles are only congruent if all of their sides are the same length, and all of the corresponding angles are of the same degree. Luckily, we only need three of these six numbers to completely determine the others, as long as we have at least one angle and one side, and any other combination of the other numbers.
In this case, we have two adjacent angles and one side, directly across from one of our angles in both triangles. This can be called the AAS case. We can see from our picture that all of our angles match, and the two sides match as well. They're all in the same position relative to each other on the triangle, so that is enough information to say that the two triangles are congruent.
Example Question #173 :Plane Geometry
Two similiar triangles have a ratio of perimeters of
If the smaller triangle has sides of 3, 7, and 5, what is the perimeter of the larger triangle.
Adding the sides gives a perimeter of 15 for the smaller triangle. Multipying by the given ratio of
Example Question #174 :Plane Geometry
Two similiar triangles exist where the ratio of perimeters is 4:5 for the smaller to the larger triangle. If the larger triangle has sides of 6, 7, and 12 inches, what is the perimeter, in inches, of the smaller triangle?
18
25
23
20
20
The larger triangle has a perimeter of 25 inches. Therefore, using a 4:5 ratio, the smaller triangle's perimeter will be 20 inches.
Example Question #175 :Plane Geometry
Two similar triangles' perimeters are in a ratio of
1. Find the perimeter of the larger triangle:
2. Use the given ratio to find the perimeter of the smaller triangle:
Cross multiply and solve:
Example Question #176 :Plane Geometry
There are two similar triangles. Their perimeters are in a ratio of
Use proportions to solve for the perimeter of the larger triangle:
Cross multiply and solve:
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