All Questions ⁺⁰236027 Questions

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Geometry

Square ABCD has side length 1. Point $P$ lies on $\overline{BC}$ and point $Q$ lies on $\overline{CD}$ such that $\angle PAQ = 45^\circ.$ The area of triangle BPQ is $\frac{7}{47}.$ Compute the area of triangle APQ.

cooIcooIcooI17 Dec 18, 2024

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+606

Geometry

A straight line \ell divides a triangle \Delta into two congruent triangles. Select all the statements that must be true.

- Triangle $\Delta$ has three equal sides.
- Triangle $\Delta$ read more ..

cooIcooIcooI17 Dec 18, 2024

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+893

Geometry

In pentagon ABCDE, \overline{AC} bisects \angle BCE and $\overline{AD}$ bisects $\angle BDE.$ If $\angle CBD = 30^\circ$ and $\angle CED = 60^\circ,$ then find $\angle CAD,$ in degrees.

AnswerscorrectIy Dec 18, 2024

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+893

Geometry

In the diagram, \overline{BE} bisects \angle ABC, and $\overline{CE}$ bisects $\angle ACD.$ Compute $\angle BAC,$ in degrees.

AnswerscorrectIy Dec 18, 2024

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+893

Geometry

Two angle bisectors of triangle ABC, $\overline {BE}$ and $\overline {CF}$, intersect at $P$. What is $\angle A$ in degrees?

AnswerscorrectIy Dec 18, 2024

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+893

Geometry

Point X is on side \overline{AC} of triangle $ABC$ such that $\angle AXB =\angle ABX + 20^\circ$, and $\angle ABC - \angle BAC = 36^\circ$. Find $\angle XBC$ in degrees.

AnswerscorrectIy Dec 18, 2024

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+510

Geometry

A robot moved 10 meters towards north. It then turned 45^\circ to its right and moved another 15 meters. It then turned 45^\circ to its left and moved another 20 meters. Last, it turned x^\circ to its right. The robot was facing south after the last move. read more ..

onyuIee Dec 18, 2024

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+510

Geometry

What is the measure (in degrees) of the smallest [b]interior[/b] angle of a triangle in which the exterior angle measures have the ratio 4:2:8?

onyuIee Dec 18, 2024

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+510

Geometry

In triangle ABC, the angles $\angle A,$ $\angle B,$ $\angle C$ form an arithmetic sequence. If \angle A = 60^\circ, then what is $\angle C,$ in degrees?

onyuIee Dec 18, 2024

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+510

Geometry

In the diagram, what is the measure of \angle ACB in degrees?

onyuIee Dec 18, 2024

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+510

Geometry

Given that \ell \parallel m, find $\angle XYZ + \angle XZY,$ in degrees.

onyuIee Dec 18, 2024

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+510

Geometry

The three angles of a triangle have measures $2x + 3y$ degrees, $8x + 15y$ degrees, and $4x - 2y$ degrees. Find $x$ (in degrees).

onyuIee Dec 18, 2024

Dec 17, 2024

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+411

Geometry

In the diagram below, $\overline{PQ}$ and $\overline{TU}$ are parallel, and $Q$, $R$, and $S$ are collinear. What is the degree measure of $\angle RTU$?

crimefightingvigiI Dec 17, 2024

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+411

Geometry

In the diagram below, \angle BAG = 170^\circ, $\angle EAF = 2x$, and $\angle CAD = 6x.$ Find angle $x$, in degrees.

crimefightingvigiI Dec 17, 2024

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+411

Geometry

Given that \overline{DJ} \parallel \overline{KE}, $\angle DBF = 35^\circ$, and $\angle ABC = 55^\circ$, find the measure of $\angle GCE$ in degrees.

crimefightingvigiI Dec 17, 2024

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+411

Geometry

What is the number of degrees in the smaller angle formed by the hour and minute hands of a clock at 9:30?

crimefightingvigiI Dec 17, 2024

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+411

Geometry

What is the number of degrees in the smaller angle formed by the hour and minute hands of a clock at $4{:}15?$

crimefightingvigiI Dec 17, 2024

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+411

Geometry

In the diagram below, lines $AB$ and $ED$ are parallel. Find angle $\angle CDE,$ in degrees.

crimefightingvigiI Dec 17, 2024

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+411

Geometry

Lines $AB$ and $CD$ intersect at a point $O$ in such a way that the measure of $\angle AOC$ is $4$ times the measure of $\angle AOB$. What is the measure of $\angle AOC,$ in degrees?

crimefightingvigiI Dec 17, 2024

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+411

Geometry

The diagram below is drawn to scale. Select all the obtuse angles. read more ..

crimefightingvigiI Dec 17, 2024

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+411

Geometry

The two horizontal lines in the diagram below are parallel. We are also given the measure of one angle in the diagram. Find the value of $c,$ in degrees.

crimefightingvigiI Dec 17, 2024

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+411

Geometry

Suppose instead of measuring an angle the "regular" way, we go around the "long" way, as shown in the diagram.
The "regular" angle $XYZ$ has measure $90^{\circ}.$ What is the measure of the "long" way around angle, in degrees?
<read more ..

crimefightingvigiI Dec 17, 2024

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+411

Geometry

How many labeled points are on ray $\overrightarrow{AC}$ below?

crimefightingvigiI Dec 17, 2024

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