Question

the measure of each angle of an isosceles triangle is
select one:
a. 5
b. 90
c. 30
d. 15
e. none of these

the total number of diagonals in a hexagon is
select one:
a. 3
b. 9
c. 6
d. 30

Explanation:

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First Question:

Step1: Recall isosceles triangle rules

An isosceles triangle has at least two equal angles, and the sum of all interior angles is $180^\circ$. No single fixed angle measure applies to all isosceles triangles (e.g., a 45-45-90 triangle, 70-70-40 triangle, etc. are all valid isosceles triangles).

Step2: Evaluate given options

The options a-d provide a single angle measure as if it applies to all isosceles triangles, which is incorrect.
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Second Question:

Step1: Use diagonal count formula

For an $n$-sided polygon, the number of diagonals is given by $\frac{n(n-3)}{2}$. A hexagon has $n=6$ sides.

Step2: Substitute $n=6$ into formula

$$\frac{6(6-3)}{2} = \frac{6 \times 3}{2} = 9$$

Answer:

1. e. none of these
2. b. 9