Question

1 name the following types of angles. choose from acute, right, obtuse, straight, reflex or revolution.
2 find the value of (a).
3 identify the following triangles as equilateral, isosceles or scalene.
4 identify the following as right, acute or obtuse triangles.
5 find any missing angles in these triangles.
6 of the six special quadrilaterals (square, rectangle, parallelogram, rhombus, kite and trapezium), which ones match the following descriptions?
a two pairs of equal length sides
b two pairs of parallel sides
c equal length diagonals
7 find the value of the pronumerals in each of the following.
8 name the following shapes.

Explanation:

Classify angles in Question 1

We classify each angle based on its measure:

• a: \(110^\circ\) is between \(90^\circ\) and \(180^\circ\), which is obtuse.
• b: \(33^\circ\) is between \(0^\circ\) and \(90^\circ\), which is acute.
• c: \(215^\circ\) is between \(180^\circ\) and \(360^\circ\), which is reflex.
• d: The square symbol indicates a right angle (\(90^\circ\)).
• e: A straight line represents a straight angle (\(180^\circ\)).
• f: A full circle represents a revolution (\(360^\circ\)).

Solve for unknowns in Question 2

We apply geometric angle relationships:

• a: The two angles form a right angle (\(90^\circ\)):

$$a + 55 = 90 \implies a = 35$$

• b: Vertically opposite angles are equal:

$$a = 38$$

• c: Angles on a straight line add up to \(180^\circ\), or angles at a point add up to \(360^\circ\). Here, the straight line is split by the \(100^\circ\) angle and \(a^\circ\):

$$a + 100 = 180 \implies a = 80$$

Classify triangles in Question 3 and 4

We classify triangles by side lengths and angles:

• 3a: Two sides are marked equal, so it is isosceles.
• 3b: All three angles are \(60^\circ\), so it is equilateral.
• 3c: All three sides have different lengths, so it is scalene.
• 4a: One angle is clearly greater than \(90^\circ\), so it is obtuse.
• 4b: All angles are less than \(90^\circ\), so it is acute.
• 4c: One angle is marked with a right-angle square, so it is right.

Find missing angles in Question 5

The sum of interior angles in any triangle is \(180^\circ\):

• a: Let the missing angle be \(x\):

$$x + 40 + 80 = 180 \implies x = 60$$

• b: The triangle is a right-angled triangle (indicated by the square symbol):

$$x + 90 + 30 = 180 \implies x = 60$$

• c: The triangle is a right-angled triangle:

$$x + 90 + 40 = 180 \implies x = 50$$

Identify quadrilaterals and parallel lines in Questions 6, 7, and 8

For Question 6, we match descriptions to special quadrilaterals:

• a (Two pairs of equal length sides): Parallelogram, rectangle, square, rhombus, kite.
• b (Two pairs of parallel sides): Parallelogram, rectangle, square, rhombus.
• c (Equal length diagonals): Rectangle, square.

For Question 7, we use parallel line angle properties:

• a: Vertically opposite angles are equal, so \(a = 60\).
• b: Co-interior angles add up to \(180^\circ\):

$$b + 110 = 180 \implies b = 70$$

• c: Vertically opposite angles give \(a = 60\). Alternate angles give \(b = 60\).

For Question 8, we name the polygons:

• a: A five-sided polygon is a pentagon.
• b: A quadrilateral with two pairs of parallel sides is a parallelogram.
• c: A quadrilateral with one pair of parallel sides is a trapezium.

Answer:

Question 1

• a: Obtuse
• b: Acute
• c: Reflex
• d: Right
• e: Straight
• f: Revolution

Question 2

• a: \(a = 35\)
• b: \(a = 38\)
• c: \(a = 80\)

Question 3

• a: Isosceles
• b: Equilateral
• c: Scalene

Question 4

• a: Obtuse
• b: Acute
• c: Right

Question 5

• a: \(60^\circ\)
• b: \(60^\circ\)
• c: \(50^\circ\)

Question 6

• a: Parallelogram, rectangle, square, rhombus, kite
• b: Parallelogram, rectangle, square, rhombus
• c: Rectangle, square

Question 7

• a: \(a = 60\)
• b: \(b = 70\)
• c: \(a = 60\), \(b = 60\)

Question 8

• a: Pentagon
• b: Parallelogram
• c: Trapezium