Mel draws a line segment AB. Then, with A as the center and AB as the radius, she draws a semicircle. Taking the same radius and with B as the center, she draws two arcs on either side of AB intersecting the semicircle at the points C and D. What is the measure of $∠ C A D$ ?

150^{\circ}

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60^{\circ}

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120^{\circ}

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90^{\circ}

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Solution

The correct option is C $120^{\circ}$

From the steps of construction, we can see that $∠ C A B = 60^{\circ}$ and $∠ D A B = 60^{\circ}$ .

Hence, $∠ C A D = ∠ C A B + ∠ D A B = 60^{\circ} + 60^{\circ} = 120^{\circ}$

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Q. John draws line segment AB, then with A as the center and AB as the radius, he draws a semicircle. Taking the same radius and with B as the center, he draws another two arcs intersecting the semi-circle at the points C and D. What is the measure of

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Q. Zain draws a line segment AB. Then, taking A as the center and AB as the radius, he draws a semicircle above AB. Taking the same radius and B as the center, he draws a curve that intersects the semicircle. From the point of intersection, with the same radius, he draws a curve that intersects the semicircle at another place and marks it as C. What is the angle formed by ABC?

Q. A few construction steps are given below. Using the given information, find the value of

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Step 1: Draw a line segment AB.
Step 2: With A as the center and radius more than half of AB on the compass, draw arcs above and below AB.
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Q. Steps for the construction of

90^{\circ}

is given below. Choose the correct order.

1.With P as the centre and radius more than half of PQ, draw an arc above the line segment AB
2.With O as the centre, draw semicircle with suitable radius that cuts line segment AB at point P and Q.
3.With Q as the centre and with same radius as in previous step, draw another arc, which cuts the previous arc. Name the point of intersection as C
4.Draw a line segment AB, mark a point 'O' on it.
5.Join points O and C using a scale and a pencil and extend to get ray OC

Draw a circle with radius $4 c m$ and center P. Draw another circle of same radius and with center at Q such that it intersects the previous circle. Join PQ. Now join the points of intersection and name this line segment as AB. Mark the point of intersection of AB and PQ as O.

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Mel draws a line segment AB. Then, with A as the center and AB as the radius, she draws a semicircle. Taking the same radius and with B as the center, she draws two arcs on either side of AB intersecting the semicircle at the points C and D. What is the measure of ∠CAD?

The correct option is C 120∘ From the steps of construction, we can see that ∠CAB=60∘ and ∠DAB=60∘. Hence, ∠CAD=∠CAB+∠DAB=60∘+60∘=120∘

Mel draws a line segment AB. Then, with A as the center and AB as the radius, she draws a semicircle. Taking the same radius and with B as the center, she draws two arcs on either side of AB intersecting the semicircle at the points C and D. What is the measure of $∠ C A D$ ?

The correct option is C $120^{\circ}$

From the steps of construction, we can see that $∠ C A B = 60^{\circ}$ and $∠ D A B = 60^{\circ}$ .

Hence, $∠ C A D = ∠ C A B + ∠ D A B = 60^{\circ} + 60^{\circ} = 120^{\circ}$