In quadrilateral ABCD, one side is produced to form an exterior angle. ∠D=80∘D=80^\circD=80∘, ∠C=97∘C=97^\circC=97∘ and the exterior angle at B is 57°. Calculate ∠A, giving a reason for each step.
PQRS is a parallelogram, with one side produced to form an exterior angle. The exterior angle at P is 61°. Calculate ∠R, giving a reason for each step.
△XYZ is similar to △PQR (the triangles are equiangular). XY=6XY=6XY=6 cm, YZ=10YZ=10YZ=10 cm and PQ=15PQ=15PQ=15 cm. Calculate the length of QR.
PQRS is a parallelogram, with one side produced to form an exterior angle. The exterior angle at P is 63°. Calculate ∠Q, giving a reason for each step.
ABCD is a parallelogram, with one side produced to form an exterior angle. The exterior angle at A is 63°. Calculate ∠B, giving a reason for each step.
△ABC is similar to △RST (the triangles are equiangular). AB=14AB=14AB=14 cm, BC=14BC=14BC=14 cm and RS=21RS=21RS=21 cm. Calculate the length of ST.
PQRS is a parallelogram, with one side produced to form an exterior angle. The exterior angle at P is 53°. Calculate ∠Q, giving a reason for each step.
PQRS is a parallelogram, with one side produced to form an exterior angle. The exterior angle at P is 92°. Calculate ∠Q, giving a reason for each step.
In quadrilateral ABCD, one side is produced to form an exterior angle. ∠D=64∘D=64^\circD=64∘, ∠B=100∘B=100^\circB=100∘ and the exterior angle at C is 61°. Calculate ∠A, giving a reason for each step.
△RST is similar to △XYZ (the triangles are equiangular). RS=12RS=12RS=12 cm, ST=18ST=18ST=18 cm and XY=18XY=18XY=18 cm. Calculate the length of YZ.
ABCD is a parallelogram, with one side produced to form an exterior angle. The exterior angle at A is 76°. Calculate ∠C, giving a reason for each step.
In quadrilateral KLMN, one side is produced to form an exterior angle. ∠K=120∘K=120^\circK=120∘, ∠M=61∘M=61^\circM=61∘ and the exterior angle at N is 118°. Calculate ∠L, giving a reason for each step.
