Answer:
m∠P = 82°
m∠Q = 49°
m∠R = 49°
Step-by-step explanation:
<em>In the isosceles triangle, the base angles are equal in measures</em>
In Δ PQR
∵ PQ = PR
∴ Δ PQR is an isosceles triangle
∵ ∠Q and ∠R are the base angles
→ By using the fact above
∴ m∠Q = m∠R
∵ m∠Q = (3x + 25)°
∵ m∠R = (2x + 33)°
→ Equate them
∴ 3x + 25 = 2x + 33
→ Subtract 2x from both sides
∵ 3x - 2x + 25 = 2x - 2x + 33
∴ x + 25 = 33
→ Subtract 25 from both sides
∵ x + 25 - 25 = 33 - 25
∴ x = 8
→ Substitute the value of x in the measures of angles Q and R
∵ m∠Q = 3(8) + 25 = 24 + 25
∴ m∠Q = 49°
∵ m∠R = 2(8) + 33 = 16 + 33
∴ m∠R = 49°
∵ The sum of the measures of the interior angles of a Δ is 180°
∴ m∠P + m∠Q + m∠R = 180°
→ Substitute the measures of angles Q and R
∵ m∠P + 49 + 49 = 180
∴ m∠P + 98 = 180
→ Subtract 98 from both sides
∵ m∠P + 98 - 98 = 180 - 98
∴ m∠P = 82°
Triangles = 180 degrees
Angle 1 = 30 degrees
Angle 2 = 40 degrees
Therefore 180 - 30 - 40 = 110 degrees = Angle 3
It is correct that given two angles of a triangle, the third angle must be 180 degrees - the other two angles. So Adeline’s triangle will have the same angles.
However, Solomon’s triangle & Adeline’s triangle could be vastly different sizes. And since that’s possible, the two triangles cannot be guaranteed to be congruent.
Answer:
$120 in interest
Step-by-step explanation:
The formula for finding how much interest you get over time is this :
Principal × Rate × Time = Interest you get at the end
Principal is how much you start out with, so in this case that's $1,000.
Rate is the percent annual interest, which in this case is 6%.
Last, time, time in this case is 2 years.
I = (1000)(0.06)(2) = 120
I will get $120 in interest.
Answer:( x ) = 5 x 3 - 4 .
Step-by-step explanation:
(x-2)/6 = (3x-2)/5
(x-2)*5 = (3x-2)*6
5х-10=18х-12
13х=2
х=2/13
