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
Answer:
6=72 cm; 7=15 cm; 8=30 in; 9)56.5 degrees; 10)40 in
Step-by-step explanation:
6) The height of the triangle is 12 cm. The base is around 10 cm. Triangles are 1/2(b)h, so:
1/2(10)=5
5*12=60 cm
72 is closest to this.
7) Volume is l*w*h, so:
2.5*1.5=3.75
3.75*4=15 cm
8) Again, the height is 5 and the base is 12. 1/2(b)h means:
1/2(12)=6
6*5=30 in
9) All triangles have 180 degrees. So first, add the degrees you know:
33.5+90=123.5
Now, subtract that from 180:
180-123.5=56.5
10) Trapezoids can be found by multiplying the height by the smaller base, so:
6*8=40 in
Hope this helped!
Answer:
that would be 7.33
Step-by-step explanation:
sorry it's 66
I divided 3 by 22 instead of multiplying
Answer:
x=70°
y=30°
z=20°
Step-by-step explanation:
You first need to find y, which would be 30 because the sum of the first two angles is 150, and a triangle has 180 degrees, so 180-150=30.
By finding y, we can now find a, because if you take the entire triangle, y+z must equal 50. So, z=20 because 30+z=50.
And finally, we can find x to be 70 since the sum of the two other angles is 110 and 180-110=70.
