Every angle has a measure, and this lesson is about naming angles correctly, classifying them by their measure, and finding unknown measures. Two tools do most of the work: the Angle Addition Postulate, which splits one angle into the sum of its parts, and the angle bisector, which splits an angle into two congruent angles (equal in measure).
What you are looking at: One angle, ∠ABC. The vertex is B, the fixed ray goes from B through A, and the moving ray goes from B through C. The gold wedge and the arc show the angle being measured.
What to do: Drag the orange handle on point C to change the angle. With no kind chosen, you can drag to any angle from 1° to 180°. The kind buttons under the diagram each choose a kind of angle, and the line directly above them explains how the chosen kind limits dragging.
What to notice: The measure is measured from the geometry of the two rays, and the name ∠ABC keeps the vertex B in the middle. Watch the classification change as the measure passes 90°.
Kind buttons — choosing a button moves the ray to an example of that kind and chooses that kind. With Acute chosen, you can drag only from 1° to 89°; with Obtuse chosen, only from 91° to 179°. Right and Straight are exact, so the angle cannot be dragged while one of them is chosen. Choose the same button again to turn the kind off and drag freely from 1° to 180°.
What you are looking at: ∠RST with vertex S and a ray from S through P in its interior. The interior ray splits ∠RST into two adjacent angles, ∠RSP and ∠PST. Each part has its own gold wedge and its own measure label, written with three-point names because vertex S hosts more than one angle.
What to do: Drag the purple handle on point P to move the interior ray, and drag the orange handle on point T to change the size of the whole angle. The interior ray must stay inside ∠RST: a drag that would push it onto or past either side is refused.
What to notice: However you drag, the two parts always add to the whole — that is the Angle Addition Postulate, m∠RSP + m∠PST = m∠RST, with the actual measures shown in the readout.
What you are looking at: ∠NML with vertex M and a ray from M through P in its interior. The interior ray splits ∠NML into two adjacent angles, ∠NMP and ∠PML. Each part has its own gold wedge and its own measure label, written with three-point names because vertex M hosts more than one angle. When the two parts have equal measures, ray MP is an angle bisector of ∠NML.
What to do: Drag the purple handle on point P to move the interior ray, and drag the orange handle on point L to change the size of the whole angle. The interior ray must stay inside ∠NML: a drag that would push it onto or past either side is refused. The button under the diagram is explained by the line directly above it.
What to notice: The readout always states whether ray MP bisects ∠NML. It does exactly when the two parts are congruent (equal in measure), and then each part measures half of the whole angle. When the two parts are equal, the readout box turns green and the same tick mark appears across the arc of each part of the angle.
Place the Bisector button — moves ray MP for you to exactly half of ∠NML, so you can see the two parts become equal in measure.
What to do: Each item gives you a figure and a question about it. Work in three steps: (1) choose the equation to use to solve the problem, (2) solve for x or find the missing measure, and (3) report the measure the question actually asks for. The gold wedge in the diagram always sits in the part the current step asks about. Each choice you pick moves a ray in the diagram to the position that choice describes, whether the choice is right or wrong, so you can see what the choice means; a missed choice is shown as a dashed ghost ray. A first miss gives a hint and another try, with the missed choice removed. A second miss on a step names the correct choice and explains it, and the activity then moves on. When all three steps are complete, the full worked solution appears. Press New Item for the next problem: the four problems take turns in order, and the problem number is shown with the step question.
Ready to practice? Work through these six questions, one at a time. If your first answer is wrong, you will get a hint and another try; the full explanation appears once you answer correctly, or after a second miss. Your score counts first-try answers.
Angle Measurement — Mr. J Geometry. All activities on this page run entirely in your browser.