How to find an angle in an acute / obtuse isosceles triangle

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Math › How to find an angle in an acute / obtuse isosceles triangle

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An isoceles triangle has a base angle that is twice the vertex angle. What is the sum of the base and vertex angles?

Explanation

All triangles have degrees. An isoceles triangle has one vertex angle and two congruent base angles.

Let vertex angle and base angle.

So the equation to solve becomes:

Thus for the vertex angle and for the base angle.

The sum of the vertex and one base angle is .

An isoceles triangle has a base angle that is degrees less than three times the vertex angle. What is the product of the vertex angle and the base angle?

Explanation

Every triangle has 180 degrees. An isoceles triangle has one vertex angle and two congruent base angles.

Let vertex angle and base angle.

Then the equation to solve becomes:

, or .

Then the vertex angle is , the base angle is , and the product is .

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?

Explanation

Every triangle has . An isosceles triangle has one vertex ange, and two congruent base angles.

Let be the vertex angle and be 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 .

An isoceles triangle has a vertex angle that is degrees more than twice the base angle. What is the vertex angle?

Explanation

Every triangle has degrees. An isoceles triangle has one vertex angle and two congruent base angles.

Let base angle and vertex angle.

So the equation to solve becomes .

Thus the base angles are and the vertex angle is .

You are flying a kite at an altitude of 40 feet after having let out 75 feet of string. What is the kite's angle of elevation from where you are holding the spool of string at a height of 4 feet off the ground? Round answer to one decimal place.

$28.7^{o}$

$25.6^{o}$

$65.8^{o}$

$45.3^{o}$

Explanation

First, we must draw a picture to include all important parts given in the problem.

Kite1

Once this is determined we can use trigonometry to find the angle of elevation.

$sin(x)=\frac{36}{75}$

Use the inverse sin on a calculator to solve.

$sin^{-1}\left (sin(x) \right )=sin^{-1}\left (\frac{36}{75} \right )$

$x=28.7^{0}$

If an isosceles triangle has an angle measuring greater than 100 degrees, and another angle with a measuring degrees, which of the following is true?

Explanation

In order for a triangle to be an isosceles triangle, it must contain two equivalent angles and one angle that is different. Given that one angle is greater than 100 degrees: Thus, the sum of the other two angles must be less than 80 degrees. If an angle is represented by :

Isosceles

Refer to the above triangle. By what statement does it follow that $\angle B \cong \angle C$ ?

The Isosceles Triangle Theorem

The Converse of the Isosceles Triangle Theorem

The Side-Side-Side Postulate

The Side-Angle-Side Postulate

The Pythagorean Theorem

Explanation

We are given that, in $\bigtriangleup ABC$ , two sides are congruent; specifically, $\overline{AB} \cong\overline{AC}$ . It is a consequence of the Isosceles Triangle Theorem that the angles opposite the sides are also congruent - that is, $\angle B \cong \angle C$ .

In an obtuse isosceles triangle the angle measurements are, $x^\circ$ , $x^\circ$ , and $(10x-2)=128^\circ$ . Find the measurement of one of the acute angles.

$13^\circ$

$26^\circ$

$32^\circ$

$4^\circ$

$10^\circ$

Explanation

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.

The solution is:

However, degrees is the measurement of both of the acute angles combined.

Each individual angle is $26\div2=13$ .

Triangle FGH has equal lengths for FG and GH; what is the measure of ∠F, if ∠G measures 40 degrees?

140 degrees

70 degrees

40 degrees

100 degrees

None of the other answers

Explanation

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.

Angle G for this triangle 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.

An isosceles triangle has a vertex angle that is twenty degrees more than twice the base angle. What is the sum of the vertex and base angles?