Self Practice 2025-01-24 Written Sol

[PSMO S1.11.01]

What is the sum of the interior angles of a convex 10-gon?

[PSMO S1.11.02]

Given that one interior angle of a quadrilateral is 56°, the second interior angle is twice as large, and the third interior angle is 10° smaller than the second interior angle. Find the degree of the fourth interior angle.

[PSMO S1.11.03]

As shown in figure, ∠A = 80°, and the bisectors of ∠ABC and the exterior angle of ∠ACB intersect at D. Find the size of ∠D.

[PSMO S1.11.04]

As shown in figure, find the degree of ∠A + ∠B + ∠C + ∠D + ∠E.

[PSMO S1.11.01]

What is the sum of the exterior angles of a pentagon?

[PSMO S1.11.05]

As shown in figure, find the degree of ∠A + ∠B + ∠C + ∠D + ∠E.

[PSMO S1.11.06]

As shown in figure, find the degree of ∠A + ∠B + ∠C + ∠D + ∠E + ∠F.

[PSMO S1.11.07]

As shown in figure, a straight line intersects the sides and extended sides of △ABC at D, E, and F. ∠A = 20°, ∠CED = 100°, and ∠ADF = 35°. Find the degree of ∠B.

[PSMO S1.11.13]

There is a pentagon. Its first interior angle is 20° smaller than its second interior angle, its second interior angle is 20° smaller than its third interior angle, its fourth interior angle is 20° smaller than its fifth interior angle. Find the degree of its third interior angle.

[PSMO S1.12.05]

As shown in figure, AB || CD, ∠1 = ∠2, and ∠EFD = 70◦. Find the degree of ∠D.