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 $∠$ CAD?

60^{\circ}

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150^{\circ}

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90^{\circ}

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120^{\circ}

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Solution

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

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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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 ∠CAD?

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

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 $∠$ CAD?

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

From the steps of construction,
we can see that $∠ C A B = 60^{\circ}$ and $∠ D A B = 60^{\circ}$ .
Hence, $∠ C A D = ∠ C A B + ∠ D A B = 60^{\circ} + 60^{\circ} = 120^{\circ}$