All ACT Math Resources
Example Questions
Example Question #11 :Acute / Obtuse Isosceles Triangles
A和B点躺在一个圆集中在Z,在哪儿e central angle
30°
15°
25°
Cannot be determined from the given information
20°
20°
Because line segments ZA and ZB are radii of the circle, they must have the same length. That makes triangle ABZ an isosceles triangle, with 140 + 2x = 180-->2x = 40-->x = 20
Example Question #1 :How To Find An Angle In An Acute / Obtuse Isosceles Triangle
Triangle FGH has equal lengths for FG and GH; what is the measure of∠F, if∠G measures 40 degrees?
None of the other answers
140 degrees
40 degrees
100 degrees
70 degrees
70 degrees
It's good to draw a diagram for this; we know that it's an isosceles triangle; remember that the angles of a triangle total 180 degrees.
角G特里安gle is the one angle that doesn't correspond to an equal side of the isosceles triangle (opposite side to the angle), so that means∠F =∠H, and that∠F +∠H + 40 = 180,
By substitution we find that∠F * 2 = 140 and angle F = 70 degrees.
Example Question #1 :Isosceles Triangles
The vertex angle of an isosceles triangle is.What is the base angle?
An isosceles triangle has two congruent base angles and one vertex angle. Each triangle contains.Let= base angle, so the equation becomes.年代olving forgives
Example Question #32 :Isosceles Triangles
在一个isosceles triangle the base angle is five less than twice the vertex angle. What is the sum of the vertex angle and the base angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let= the vertex angle
and= base angle
年代o the equation to solve becomes
or
Thus the vertex angle is 38 and the base angle is 71 and their sum is 109.
Example Question #31 :Isosceles Triangles
年代idesandin this triangle are equal. What is the measure of?
This triangle has an angle of.我们也知道有另一个角度atbecause the two sides are equal. Adding those two angles together gives ustotal. Since a triangle hastotal, we subtract 130 from 180 and get 50.
Example Question #223 :Act Math
An isosceles triangle has a base angle that is six more than three times the vertex angle. What is the base angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let= vertex angle and= base angle.
Then the equation to solve becomes
or
.
年代olving for给出了一个顶角angl 24度和基地e of 78 degrees.
Example Question #2 :How To Find An Angle In An Acute / Obtuse Isosceles Triangle
The base angle of an isosceles triangle is thirteen more than three times the vertex angle. What is the difference between the vertex angle and the base angle?
Every triangle has.An isosceles triangle has one vertex ange, and two congruent base angles.
Letbe the vertex angle andbe the base angle.
The equation to solve becomes, since the base angle occurs twice.
Now we can solve for the vertex angle.
The difference between the vertex angle and the base angle is.
Example Question #3 :How To Find An Angle In An Acute / Obtuse Isosceles Triangle
A particular acute isosceles triangle has an internal angle measuring.Which of the following must be the other two angles?
By definition, an acute isosceles triangle will have at least two sides (and at least two corresponding angles) that are congruent, and no angle will be greater than.Addtionally, like all triangles, the three angles will sum to.Thus, of our two answers which sum to, onlyis valid, aswould violate the "acute" part of the definition.
Example Question #2021 :Hspt Mathematics
In triangle ABC, Angle A = x degrees, Angle B = 2x degrees, and Angle C = 3x+30 degrees. How many degrees is Angle B?
30°
105°
50°
45°
25°
50°
Because the interior angles of a triangle add up to 180°, we can create an equation using the variables given in the problem: x+2x+(3x+30)=180. This simplifies to 6X+30=180. When we subtract 30 from both sides, we get 6x=150. Then, when we divide both sides by 6, we get x=25. Because Angle B=2x degrees, we multiply 25 times 2. Thus, Angle B is equal to 50°. If you got an answer of 25, you may have forgotten to multiply by 2. If you got 105, you may have found Angle C instead of Angle B.