Question

What is the value of x

Answer 1

Answer:

90°

Step-by-step explanation:

The polygon has 7 sides, so the total of internal angles will be ...

... 180°×(7 -2) = 900°

The sum is then ...

... x + 146° +122° +142° +140° +110° +142° = 900°

... x + 802° = 900° . . . . . simplify

... x = 98° . . . . . . . . . . . . .subtract 802°

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Comment on angle measure formula

The usual formula for computing the total of internal angles of a convex polygon with n sides is ...

... total angle measure = (n -2)×180°

This can be simplified from the fact that the sum of external angles is always 360°. That is, for internal angles a1, a2, ..., an, the sum of external angles is ...

... (180° -a1) +(180° -a2) +... +(180° -an) = 360°

... n×180° -(a1 +a2 +... +an) = 360° . . . . . . collect terms

... n×180° -360° = (a1 +a2 +... +an) . . . . . . add ∑ak -360°

... 180°×(n -2) = a1 +a2 +... +an . . . . . . . . . factor out 180°