Mathematics 7th grade | UNIT 5: Angles 5.2 Drawing and measuring angles
You need to use a protractor to draw and measure reflex angles.
How to draw an angle of ${245^ \circ }$
If you have a protractor that measures angles up to ${360^ \circ }$ you can measure ${245^ \circ }$ directly. If your protractor only goes up to ${180^ \circ }$, use one of these methods.
Method 1: ${245^ \circ } - {180^ \circ } = {65^ \circ }$. Measure ${180^ \circ }$
(half a turn) and then another ${65^ \circ }$.
Method 2: A whole turn is ${360^ \circ }$ and
${360^ \circ } - {245^ \circ } = {115^ \circ }$.
Measure an obtuse angle of ${115^ \circ }$ and the reflex, angle between the two lines will be ${245^ \circ }$.
${180^ \circ } + {65^ \circ } = {245^ \circ }$
You can use a similar method to measure a reflex angle. Either divide it into ${180^ \circ } + $ another angle, or measure the smaller angle between the two line segments and subtract it from ${360^ \circ }$.
Exercise 5.2
1) Estimate the size of each of these angles. Then measure each one to see how close you were to the correct answer.
2) Draw angles of the following sizes.
a: ${62^ \circ }$
b: ${157^ \circ }$
c: ${200^ \circ }$
d: ${295^ \circ }$
e: ${19^ \circ }$
f: ${111^ \circ }$
g: ${342^ \circ }$
h: ${233^ \circ }$
3) a: Measure the angles labelled ${x^ \circ },{y^ \circ }$ and ${z^ \circ }$.
b: Explain why the angles should add up to ${360^ \circ }$. Use this fact to check your accuracy.
4) a Measure the angles labelled ${r^ \circ }$, ${s^ \circ }$ and ${t^ \circ }$.
b: The angles should add up to ${900^ \circ }$. Use this fact to check your accuracy.
c: If the triangle was equilateral, what would be the values of r, s and t? Give a reason for your answer.
5) The angles of a triangle are ${125^ \circ },{37^ \circ }$ and ${18^ \circ }$.
a: What are the reflex angles at the corners of this triangle?
b: Can you draw a triangle where one of the angles of the triangle is a reflex angle?