Answer :
Answer:
m m Step-by-step explanation: m m m To find each angle measure, find the value of x. First, get an equation that defines the relationship between the angle measures as follows: m (13x + 4)° + (10x - 1)° = 141° Use the equation to solve for x 13x + 4 + 10x - 1 = 141 Combine like terms 13x + 10x + 4 - 1 = 141 23x + 3 = 141 Subtract 3 from each side of the equation 23x + 3 - 3 = 141 - 3 23x = 138 Divide each side by 23 23x/23 = 138/23 x = 6 m Plug in the value of x m m m Plug in the value of x m m
The measure of the intersecting line angles are:
∠PQS =
∠SQR =
Given data:
The measure of angle ∠PQR = 141°
Now, the measure of angle ∠PQS = (13x + 4 )°
The measure of angle ∠SQR = (10x - 1 )°
The junction point is the place where two intersecting lines meet.
So, the measure of ∠PQS + ∠SQR = ∠PQR
Substituting the values in the equation:
141 = 13x + 4 + 10x - 1
23x + 3 = 141
Subtracting 3 on both sides:
23x = 138
Divide by 23 on both sides:
x = 6
So, the measure of ∠PQS = 82°
The measure of ∠SQR = 59°
Hence, the angles are solved.
To learn more about intersecting lines, refer:
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