An angle measures 15 more than twice it's supplement. find themeasure of it's supplement.

Faith Welch
2022-07-27
Answered

An angle measures 15 more than twice it's supplement. find themeasure of it's supplement.

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asked 2022-08-12

Existence of Right Angle in Hilbert Axioms

Hilbert, in Foundations of Geometry briefly mentions that the existence of right angles is a corollary to the supplementary angle theorem. (i.e. If two angles are congruent, then their supplementary angles are congruent).

How does existence of right angles follow from this?

Hilbert, in Foundations of Geometry briefly mentions that the existence of right angles is a corollary to the supplementary angle theorem. (i.e. If two angles are congruent, then their supplementary angles are congruent).

How does existence of right angles follow from this?

asked 2022-08-13

Prove that the intersection angle between the Simson lines of two triangles inscribed in the same circle it's the same for any point.

Suppose the triangles ABC and DEF share the circuncircle C, and P and Q are any diferent points on C. Let l, m be, the Simson lines of P related to ABC and DEF, and p, q the Simson lines of Q related to ABC and DEF, then i must prove the angle between l and m equals the angle between p and q.

I just have one Theorem about the Simson line:

Theorem: Let P, Q be two points on the circuncircle, C, of the triangle ABC. Let l, m be their respective Simson's lines. Then the angle between l an m equals to the half of the central angle POQ, where O is the center of C.

Suppose the triangles ABC and DEF share the circuncircle C, and P and Q are any diferent points on C. Let l, m be, the Simson lines of P related to ABC and DEF, and p, q the Simson lines of Q related to ABC and DEF, then i must prove the angle between l and m equals the angle between p and q.

I just have one Theorem about the Simson line:

Theorem: Let P, Q be two points on the circuncircle, C, of the triangle ABC. Let l, m be their respective Simson's lines. Then the angle between l an m equals to the half of the central angle POQ, where O is the center of C.

asked 2022-08-12

Pythagoras: Get b when only a and angle $\alpha $ are given

Given the Pythagoras Theorem: ${a}^{2}+{b}^{2}={c}^{2}$

Is there a way to get the value of b when we only have a value for a and the angle $\alpha $?

Given the Pythagoras Theorem: ${a}^{2}+{b}^{2}={c}^{2}$

Is there a way to get the value of b when we only have a value for a and the angle $\alpha $?

asked 2022-08-21

How do you find a point on a line bisecting an angle in three-dimensional space?

Given the x, y, z coordinates of three points ${P}_{1},{P}_{2},{P}_{3}$ with the angle between them being $\mathrm{\angle}{P}_{1}{P}_{2}{P}_{3}$, how do you find a point, say at a distance of 1 from ${P}_{2}$, on the line that bisects the angle?I know from the angle bisector theorem that the point must be equidistant from the the vector $({P}_{3}-{P}_{2})$ and $({P}_{1}-{P}_{2})$, but I can't seem to figure out how to find such a point in 3-space.

Given the x, y, z coordinates of three points ${P}_{1},{P}_{2},{P}_{3}$ with the angle between them being $\mathrm{\angle}{P}_{1}{P}_{2}{P}_{3}$, how do you find a point, say at a distance of 1 from ${P}_{2}$, on the line that bisects the angle?I know from the angle bisector theorem that the point must be equidistant from the the vector $({P}_{3}-{P}_{2})$ and $({P}_{1}-{P}_{2})$, but I can't seem to figure out how to find such a point in 3-space.

asked 2022-07-14

We have $AB=BC$, $AC=CD$, $\mathrm{\angle}ACD={90}^{\circ}$. If the radius of the circle is 'r' , find BC in terms of r .

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 2022-08-14

Angle chasing to show three points are collinear.

Let ABC be an acute triangle with circumcenter O and let K be such that KA is tangent to the circumcircle of $\mathrm{\u25b3}ABC$ and $\mathrm{\angle}KCB={90}^{\circ}$. Point D lies on BC such that KD||AB. Show that DO passes through A.

Let ABC be an acute triangle with circumcenter O and let K be such that KA is tangent to the circumcircle of $\mathrm{\u25b3}ABC$ and $\mathrm{\angle}KCB={90}^{\circ}$. Point D lies on BC such that KD||AB. Show that DO passes through A.