Answer:
The measure of the vertex angle is 94 degrees ⇒ A
Step-by-step explanation:
- In any triangle, the sum of the measures of its interior angle is 180°
- In the isosceles triangle, the two base angles are equal in measures
∵ In an isosceles triangle, the measure of the base angle = (2x + 5)
∵ The base angles of the isosceles triangles are equal in measures
∴ The measures of the base angles are (2x + 5), (2x + 5)
∵ The measure of the vertex angle = (5x - 1)
∵ The sum of the measure of the three angles = 180°
∴ (2x + 5) + (2x + 5) + (5x - 1) = 180
→ Add the like terms in the left side
∵ (2x + 2x + 5x) + (5 + 5 + -1) = 180
∴ 9x + 9 = 180
→ Subtract 9 from both sides
∴ 9x + 9 - 9 = 180 - 9
∴ 9x = 171
→ Divide both sides by 9 to find x
∴ x = 19
→ Substitute the value of x in the measure of the vertex angle to find it
∵ The measure of the vertex angle = 5x - 1
∴ The measure of the vertex angle = 5(19) - 1
∴ The measure of the vertex angle = 95 - 1
∴ The measure of the vertex angle = 94°
∴ The measure of the vertex angle is 94 degrees
All estimating problems make the assumption you are familar with your math facts, addition and multiplication. Since students normally memorize multiplication facts for single-digit numbers, any problem that can be simplified to single-digit numbers is easily worked.
2. You are asked to estimate 47.99 times 0.6. The problem statement suggests you do this by multiplying 50 times 0.6. That product is the same as 5 × 6, which is a math fact you have memorized. You know this because
.. 50 × 0.6 = (5 × 10) × (6 × 1/10)
.. = (5 × 6) × (10 ×1/10) . . . . . . . . . . . by the associative property of multiplication
.. = 30 × 1
.. = 30
3. You have not provided any clue as to the procedure reviewed in the lesson. Using a calculator,
.. 47.99 × 0.6 = 28.79 . . . . . . rounded to cents
4. You have to decide if knowing the price is near $30 is sufficient information, or whether you need to know it is precisely $28.79. In my opinion, knowing it is near $30 is good enough, unless I'm having to count pennies for any of several possible reasons.
The answer is : Prism
hope this helps !
