Teach Me Maths

Angle Facts

Question 11 mark

Which word describes the marked angle?

Hint

Compare the angle with a right angle and a straight angle.

Worked solution

Which word describes the marked angle?

  1. Acute
  2. Obtuse
  3. Reflex
  4. Right angle
  1. The marked angle is greater than a right angle but less than a straight angle.
  2. It is an obtuse angle.

Question 21 mark

Find x.

Hint

The two parts make one right angle.

Worked solution

Find x.

  1. A right angle is 90°.
  2. x=90-34=56.

Question 31 mark

Find x.

Hint

The angles together make half a turn.

Worked solution

Find x.

  1. Angles on a straight line add to 180°.
  2. x=180-67=113.

Question 42 marks

Find x.

Hint

A complete turn is 360 degrees.

Worked solution

Find x.

  1. Angles around a point add to 360°.
  2. The known angles total 95+130=225°.
  3. x=360-225=135.

Question 51 mark

Two straight lines cross. Find the angle marked x.

Hint

The marked angles are directly opposite each other.

Worked solution

Two straight lines cross. Find the angle marked x.

  1. Vertically opposite angles are equal.
  2. The angle opposite 76° is also 76°, so x=76.

Question 62 marks

Find the missing angle x in the triangle.

Hint

Add the two known angles before subtracting from the triangle total.

Worked solution

Find the missing angle x in the triangle.

  1. Angles in a triangle add to 180°.
  2. 48+69=117°, so x=180-117=63.

Question 72 marks

Find x.

Hint

The right angle already uses 90 degrees of the triangle total.

Worked solution

Find x.

  1. Angles in a triangle add to 180°.
  2. 180-90-37=53°.

Question 82 marks

The ticked sides are equal. Find x.

Hint

The two base angles are equal.

Worked solution

The ticked sides are equal. Find x.

  1. The base angles of an isosceles triangle are equal.
  2. Together they total 180-44=136°.
  3. Each is 136\div2=68°, so x=68.

Question 92 marks

Find x.

Hint

A quadrilateral can be split into two triangles.

Worked solution

Find x.

  1. Angles in a quadrilateral add to 360°.
  2. The known angles total 90+110+75=275°.
  3. The fourth is 360-275=85°.

Question 101 mark

The two marked angles are equal. Which is the reason?

Hint

Name the relationship between angles opposite each other at an intersection.

Worked solution

The two marked angles are equal. Which is the reason?

  1. The angles look the same.
  2. Angles on a straight line add to 180 degrees.
  3. Vertically opposite angles are equal.
  4. Angles in a triangle add to 180 degrees.
  1. Vertically opposite angles are equal.
  2. This rule describes angles opposite each other where two straight lines cross. It does not depend on parallel lines.

Question 113 marks

B, C and D lie on a straight line. Find angle ACD, marked x.

Hint

First find the interior angle at C, then use the straight line BCD.

Worked solution

B, C and D lie on a straight line. Find angle ACD, marked x.

  1. Angle ACB =180-51-64=65° because angles in a triangle add to 180°.
  2. Angles ACB and ACD lie on a straight line, so angle ACD =180-65=115°.

Question 122 marks

The shape is a rectangle. Find x.

Hint

Every corner of a rectangle is a right angle.

Worked solution

The shape is a rectangle. Find x.

  1. The corner totals 90°.
  2. x=90-29=61.

Question 132 marks

Find x.

Hint

Add all three known angles, then subtract from one complete turn.

Worked solution

Find x.

  1. Angles around a point add to 360°.
  2. 80+110+85=275°.
  3. x=360-275=85.

Question 143 marks

The marked angles are in the ratio a:b=2:3. Find angle a in degrees.

Hint

The five equal parts together represent a straight angle.

Worked solution

The marked angles are in the ratio a:b=2:3. Find angle a in degrees.

  1. Angles on a straight line add to 180°.
  2. There are 2+3=5 ratio parts, so each part is 180\div5=36°.
  3. The smaller angle is 2\times36=72°.

Question 153 marks

The ticked sides are equal, and AC is extended beyond C. Find x.

Hint

Find the top interior angle before using the straight-line total.

Worked solution

The ticked sides are equal, and AC is extended beyond C. Find x.

  1. The top angle is 180-57-57=66° because angles in a triangle add to 180°.
  2. Its adjacent exterior angle is 180-66=114° because angles on a straight line add to 180°.

Question 16Challenge4 marks

Triangles ABC and ACD share side AC. Find angle BCD containing AC, marked x, in degrees.

Hint

Find the angle at C in each triangle, then add the two parts.

Worked solution

Triangles ABC and ACD share side AC. Find angle BCD containing AC, marked x, in degrees.

  1. In triangle ABC, angle BCA =180-35-78=67° (angles in a triangle).
  2. In triangle ACD, angle ACD =180-46-59=75° (angles in a triangle).
  3. AC lies inside angle BCD, so angle BCD =67+75=142°.

Question 17Challenge4 marks

Find the largest angle in the triangle. Give your answer in degrees.

Hint

Add the three expressions and set their total equal to 180.

Worked solution

Find the largest angle in the triangle. Give your answer in degrees.

  1. Angles in a triangle add to 180°, so x+(x+20)+2x=180.
  2. 4x+20=180, then 4x=160 and x=40.
  3. The angles are 40°, 60° and 80°. The largest is 80°.

Question 18Challenge3 marks

The ticked sides are equal. Find the reflex angle x.

Hint

Find the top interior angle using the triangle, then use a full turn at the top vertex.

Worked solution

The ticked sides are equal. Find the reflex angle x.

  1. The base angles are equal because the two ticked sides are equal.
  2. The top interior angle is 180-73-73=34° because angles in a triangle add to 180°.
  3. Angles around a point add to 360°, so the reflex angle is x=360-34=326°.

Question 19Challenge3 marks

One side of the quadrilateral is extended. Find the exterior angle x.

Hint

First use the quadrilateral total, then the straight line at the extended side.

Worked solution

One side of the quadrilateral is extended. Find the exterior angle x.

  1. Angles in a quadrilateral add to 360°.
  2. The remaining interior angle is 360-85-90-108=77°.
  3. The interior angle and x lie on a straight line, so x=180-77=103°.

Question 20Challenge3 marks

Find the largest angle in the triangle. Give your answer in degrees.

Hint

Call each equal angle x; the third is x + 36.

Worked solution

Find the largest angle in the triangle. Give your answer in degrees.

  1. Let each equal angle be x°. Angles in a triangle give x+x+(x+36)=180.
  2. 3x+36=180, so 3x=144 and x=48.
  3. The third angle is 48+36=84°. Check: 48+48+84=180°.

More on this topic: Angle Facts worksheet with full solutions

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