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smc

geometry intermediate

Problem

The consecutive angles of a trapezoid form an arithmetic sequence. If the smallest angle is

7 5^{\circ}

, then the largest angle is

(A)

9 5^{c} i r c l e . s t r o k e d . t in y

(B)

10 0^{c} i r c l e . s t r o k e d . t in y

(C)

10 5^{c} i r c l e . s t r o k e d . t in y

(D)

11 0^{c} i r c l e . s t r o k e d . t in y

Solution

A trapezoid is a quadrilateral; therefore the interior angles sum to

36 0^{\circ}

. Thus

75 + (75 + x) + (75 + 2 x) + (75 + 3 x) = 360

, so

x = 10

and the largest angle is

10 5^{\circ}

which is

10 5^{\circ}

Final answer

C