Geometry : Construction of special angles without using protractor

**Construction
of special angles without using protractor.**

** **

__(i) Construction of angle of measure 60°__

**Step 1: **Draw a line. Mark a point** ***A*** **on it.

**Step 2: **With** ***A*** **as center draw an arc of convenient radius to
the line to meet at a point *B*.

**Step 3: **With the same radius and** ***B*** **as center** **draw an arc to cut the previous arc
at *C*.

**Step 4: **Join AC. Then** **∠*BAC*** **is the required angle with the measure
60°.

** **

__(ii) Construction of angle of measure 120°.__

We know that there are two 60° agnels in 120°. Hence, to construct 120°, we can construct two 60° angles consecutively as follows.

**Step 1: **Draw a line. Mark a point A on it.

**Step 2: **With** ***A*** **as center, draw an arc of convenient
radius to the line at a point *B*.

**Step 3: **With the same radius and** ***B*** **as center,** **draw an arc to cut the previous arc
at *C*.

**Step 4: **With the same radius and** ***C*** **as** **center,
draw an arc to cut the arc drawn in step 2 at *D*.

**Step 5: **Join AD. Then** **∠*BAD*** **is the required angle with measure 120°.

** **

__(iii) Construction of angle of measure 30°__

Since 30° is half of 60°, we can construct 30° by
bisecting the angle 60°.

**Step 1: **Construct angle 60° [Refer Construction
of angle of measure 60° (i)].

**Step 2: **With** ***B*** **as center, draw an arc of convenient
radius in the interior of ∠*BAC*.

**Step 3: **With the same radius and** ***C*** **as center, draw an arc to cut the previous arc at *D*.

**Step 4: **Join** ***AD*. Then** **∠*BAD*** **is the required angle with measure 30° [Think about ∠*DAC*?]

** **

__(iv) Construction of angle of measure 90°__

**Step 1: **Construct angle 120° [Refer Construction
of angle of measure 120° (ii)].

**Step 2: **With** ***C*** **as center, draw an arc of convenient radius in the interior of ∠*CAD*.

**Step 3: **With the same radius and D as center,
draw an arc to cut drawn in step 3 at E.

**Step 4: **Join AE. Then** **∠*BAD*** **= 90° is the required angle

Tags : Geometry | Term 1 Chapter 5 | 7th Maths , 7th Maths : Term 1 Unit 5 : Geometry

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7th Maths : Term 1 Unit 5 : Geometry : Construction of special angles without using protractor | Geometry | Term 1 Chapter 5 | 7th Maths

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