Angle Chasing: all problems

In the adjoining figure, $ABCD$ is a square, $ABE$ is an equilateral triangle and point $E$ is outside square $ABCD$. What is the measure of $\angle AED$ in degrees?

In quadrilateral $ABCD$, sides $\overline{AB}$ and $\overline{BC}$ both have length 10, sides $\overline{CD}$ and $\overline{DA}$ both have length 17, and the measure of angle $ADC$ is $60^\circ$. What is the length of diagonal $\overline{AC}$?

In $\triangle ABC$, $D$ is a point on side $\overline{AC}$ such that $BD = DC$ and $\angle BCD$ measures $70^\circ$. What is the degree measure of $\angle ADB$?

In the figure, point A is the center of the circle, the measure of angle RAS is $74^\circ$, and the measure of angle RTB is $28^\circ$. What is the measure of minor arc BR, in degrees?

The circumference of the circle with center $O$ is divided into 12 equal arcs, marked the letters $A$ through $L$ as seen below. What is the number of degrees in the sum of the angles $x$ and $y$?

Two angles of an isosceles triangle measure $70^\circ$ and $x^\circ$. What is the sum of the different possible values of $x$?

Two congruent circles centered at points $A$ and $B$ each pass through the other circle's center. The line containing both $A$ and $B$ is extended to intersect the circles at points $C$ and $D$. The circles intersect at two points, one of which is $E$. What is the degree measure of $\angle CED$?

The keystone arch is an ancient architectural feature. It is composed of congruent isosceles trapezoids fitted together along the non-parallel sides, as shown. The bottom sides of the two end trapezoids are horizontal. In an arch made with 9 trapezoids, let $x$ be the angle measure in degrees of the larger interior angle of the trapezoid. What is $x$?

In triangle ABC, AB = AC and $\angle A = 40^\circ$. The bisector from $\angle B$ intersects AC at point D. What is $\angle BDC$?

Point $P$ lies inside triangle $ABC$ such that $\angle PBC = 30^\circ$ and $\angle PAC = 20^\circ$. If $\angle APB$ is a right angle, find the measure of $\angle BCA$ in degrees.

As shown in the figure below, point $E$ lies on the opposite half-plane determined by line $CD$ from point $A$ so that $\angle CDE = 110^\circ$. Point $F$ lies on $\overline{AD}$ so that $DE = DF$, and $ABCD$ is a square. What is the degree measure of $\angle AFE$?

Concave quadrilateral ABCD is symmetric about the line AC. The measures of angles DAB and ABC are 84 degrees and 32 degrees, respectively. The dashed line segments bisect angles ABC and ADC. What is the degree measure of the acute angle at which the two dashed line segments intersect?

In triangle $ABC$, $\angle BAC$ is a right angle and $\angle ACB$ measures $34^\circ$. Let $D$ be a point on segment $BC$ for which $AC = CD$, and let the angle bisector of $\angle CBA$ intersect line $AD$ at $E$. What is the measure of $\angle BED$?

In square ABCD, point E lies on side BC and point F lies on side CD so that triangle AEF is equilateral and inside the square. Point M is the midpoint of segment EF, and P is the point other than E on AE for which PM = FM. The extension of segment PM meets segment CD at Q. What is the measure of $\angle CQP$, in degrees?