In an isosceles triangle ABC with base AC, the exterior angle at vertex C is 123 degrees. Find the angle ABC. Answer in degrees

Jamar Hays
2022-09-13
Answered

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asked 2022-08-31

Find the measure of the angle:

1. m<1 = ?

2. m<5 = ?

3. m <6 = ?

1. m<1 = ?

2. m<5 = ?

3. m <6 = ?

asked 2022-08-25

What is the measure of $\measuredangle x$ in the figure below?

For reference: In the figure shown P and Q are points of tangency and $\stackrel{\u2322}{BC}+\stackrel{\u2322}{FE}={130}^{o}.$. Calculate "x".

For reference: In the figure shown P and Q are points of tangency and $\stackrel{\u2322}{BC}+\stackrel{\u2322}{FE}={130}^{o}.$. Calculate "x".

asked 2022-08-02

Prove that if a line ${l}_{1}\ne $ l is sent to itself under a reflection through l, then ${l}_{1}$ and l intersect at right angles

asked 2022-08-14

Solution of triangles in Non-Euclidean geometry with restrictions

In triangle $ABC,AB>AC$. D is a point on AB such that $AD=AC$.

Prove that $\phantom{\rule{thinmathspace}{0ex}}\mathrm{\angle}ADC=\frac{\mathrm{\angle}B+\mathrm{\angle}C}{2}$ and $\mathrm{\angle}BCD=\frac{\mathrm{\angle}C-\mathrm{\angle}B}{2}$.

Solving this problem in Euclidean geometry is very easy. But how can it be solved with the following restrictions?

1) Parallel postulate (i.e. properties of parallel lines ) cannot be used.

2) Theorems proved using properties of parallel lines cannot be used.

3) The problem has to be solved the way euclidean geometry problems are solved. Cartesian Geometry cannot be used.

If not solvable, why cannot be?

In triangle $ABC,AB>AC$. D is a point on AB such that $AD=AC$.

Prove that $\phantom{\rule{thinmathspace}{0ex}}\mathrm{\angle}ADC=\frac{\mathrm{\angle}B+\mathrm{\angle}C}{2}$ and $\mathrm{\angle}BCD=\frac{\mathrm{\angle}C-\mathrm{\angle}B}{2}$.

Solving this problem in Euclidean geometry is very easy. But how can it be solved with the following restrictions?

1) Parallel postulate (i.e. properties of parallel lines ) cannot be used.

2) Theorems proved using properties of parallel lines cannot be used.

3) The problem has to be solved the way euclidean geometry problems are solved. Cartesian Geometry cannot be used.

If not solvable, why cannot be?

asked 2022-08-12

Finding a triangle angle based on side length equality

Consider the triangle ABC with angle A being 70 degrees, and the side lengths satisfying:

$B{C}^{2}=AC(AB+AC)$

Is there any intuitive way of finding the measure of angle B?

Consider the triangle ABC with angle A being 70 degrees, and the side lengths satisfying:

$B{C}^{2}=AC(AB+AC)$

Is there any intuitive way of finding the measure of angle B?

asked 2022-09-22

Hexagon ABCDEF has sides AB and DE of length 2, sides BC and EF of length 7, and sides CD and AF of length 11, and it is inscribed in a circle. Compute the diameter of the circle.

Why is $\overline{\mathit{A}\mathit{D}}$ the diameter of the circle?

Why is $\overline{\mathit{A}\mathit{D}}$ the diameter of the circle?

asked 2022-08-08

Prove statement: Complements of the same angle are congruent.