Classification of angles

Look at the following drawing and classify each of the indicated angles according to its type (acute, right or obtuse).

Work out quickly:

1. a) The complementary angle of $65^\circ$.
2. b) The supplementary angle of $110^\circ$.
3. c) The complementary angle of an angle of $45^\circ$.

Identify in the following chart which pair of angles are consecutive and which pair of angles are adjacent. Justify your answer based on whether or not they form a straight line.

Two streets in a Madrid neighbourhood intersect forming four angles. If angle $\hat{1}$ and angle $\hat{2}$ are adjacent, and we know that angle $\hat{1}$ is twice angle $\hat{2}$, how much does each measure? Classify both angles and explain what relationship angles $\hat{1}$ and $\hat{3}$ have based on their position.

Look at the following figure formed by two intersecting lines. If angle $A$ measures $40^\circ$, how much does angle $B$ measure knowing that they are vertically opposite? And how much do angles $C$ and $D$ measure, which are supplementary to angle $A$?

Two angles are vertically opposite. The size of one of them is given by the expression $2x + 15^\circ$ and the size of one of its adjacent angles is $x + 45^\circ$.

1. a) Calculate the value of $x$ knowing that adjacent angles are supplementary.
2. b) Determine the size of the four angles formed at the vertex and classify them all according to their size.

In a mobile solar panel, engineers need two angles to be supplementary. The first angle, which we will call $\hat{A}$, measures $72^\circ 15' 30''$.

Calculate the size of angle $\hat{B}$ so that the panel works correctly. Once calculated, state whether $\hat{B}$ is an acute, obtuse or straight angle.

An architect is designing an inclined ramp. The angle that the ramp makes with the ground (angle of elevation) is acute. It is known that its complementary angle is exactly four times the angle of elevation.

1. a) Find the size of this angle of elevation.
2. b) If the architect decides to double the slope of the ramp, what type of angle (acute, right or obtuse) will the ramp now make with the vertical (its new complementary angle)?

An analog clock shows exactly 3:00 o'clock. The hour hand is the short one (orange) and the minute hand is the long one (blue).

1. a) What type of angle do the hour hand and the minute hand form at 3:00?

1. b) If the clock advanced to 3:10, would the angle formed be acute, right or obtuse? Explain your answer.

A wall clock shows exactly 10:00 in the morning.

1. a) Calculate the size of the smaller angle formed by the hands of the clock.
2. b) Classify this angle according to its type.
3. c) What is the angle formed by the hands "on the outside" (the larger angle) called? Classify it as well.

Look at the hands of an analogue clock when they show exactly 02:40.

1. a) Calculate the convex angle formed by the hour hand and the minute hand (keep in mind that the hour hand moves proportionally to the minutes).
2. b) Calculate its supplementary angle and classify it.
3. c) At what exact time between 02:00 and 03:00 will the hands form a zero angle? (Explain your approximate answer).