11+ Missing Angles: Rules, Methods and Worked Answers

Missing-angle problems are about relationships, not how a sketch looks. A narrow-looking angle can be drawn inaccurately; a stated angle or geometric property supplies the evidence. Start by writing the rule that joins the angles you know to the angle you need.

These original explanations and questions support preparation for 11-plus exams taken in 2027. They are not official school questions or a complete syllabus. Check your target school’s current guidance. Try each question before revealing its answer; written English models illustrate a supported response rather than the only acceptable wording.

Keep four totals separate

Two different situations share 180°, but their reasons differ. The angles inside a triangle sum to 180°; adjacent angles that fill a straight angle also sum to 180°. Name the situation rather than choosing a familiar number without checking where the angles lie.

Worked example: subtract all the known parts

Three adjacent angles fill a straight angle. Two are 38° and 67°. Their combined size is 105°, leaving 180 − 105 = 75°. Check by adding 38 + 67 + 75 = 180. Subtracting only one given angle would leave a total that still includes another known part.

Worked example: use equality as well as the total

An isosceles triangle has a vertex angle of 44° between its equal sides. Its two equal base angles share 180 − 44 = 136°, so each is 68°. The word each matters: 136° is the combined remainder, not one base angle. In an equilateral triangle all three interior angles are equal, so each is 60°.

When two rules are needed

A triangle’s interior angle and an adjacent exterior angle on an extended side fill a straight angle. If the other two interior angles are 47° and 58°, the third interior angle is 75° and the adjacent exterior angle is 105°. Calculate both steps rather than assuming that the label outside the triangle belongs in the interior total.

Eight original missing-angle questions

A quick check for a convincing answer

An ordinary triangle cannot have an interior angle of 180° or more. Equal angles must have equal calculated values. The parts should add back to the named total. If any check fails, revisit the relationship before changing arithmetic at random. A correct explanation includes the rule and its application, not just the final degree symbol.

What to practise next

Use algebra basics when an unknown angle is labelled with a letter, and area and perimeter to distinguish different measurements of shapes. Return to the maths learning hub or explore original practice and worked answers.

Sources and scope

The Department for Education programme of study provides the curriculum foundation. Our examples, questions and explanations are original. This curriculum reference does not confirm the content, timing or equipment rules of any particular school’s examination.