If m∠A = (5x + 22)° and m∠B = (10x + 8)°, what is the measure of ∠B?
monkey
You said it was 10x+8 , unless we know who angle A and B are related, a definite answer cannot be found
e.g. suppose we knew that angle A = angle B, then
10x+8 = 5x+22
I would solve for x, the sub into 10x+8
To determine the measure of ∠B, we need to use the given information that m∠B = (10x + 8)°.
To find the measure of ∠B, we need to substitute the given values of ∠A and solve for x.
Given:
m∠A = (5x + 22)°
m∠B = (10x + 8)°
We know that the sum of the angles in a triangle is 180°.
∠A + ∠B + ∠C = 180°
Since we're given the measures of ∠A and ∠B, we can substitute those values in the equation:
(5x + 22)° + (10x + 8)° + ∠C = 180°
Simplify the equation by combining like terms:
15x + 30 + ∠C = 180°
Next, we need to solve for x.
15x + 30 + ∠C = 180°
15x + ∠C = 180° - 30°
15x + ∠C = 150°
Now, we are missing the measure of ∠C. Since we only have two angle measures given, we can't determine the value of ∠C. However, we can still find the value of x.
To do that, we need to use the information that the angles in a triangle add up to 180°. So, we can write the equation:
∠A + ∠B + ∠C = 180°
Substituting the given measures:
(5x + 22)° + (10x + 8)° + ∠C = 180°
Simplify the equation:
15x + 30 + ∠C = 180°
15x + ∠C = 150°
Since we can't determine the value of ∠C, we can't directly find the value of x. However, if you are given additional information, such as the measure of ∠C or any other relationships between the angles, you can solve for x and then find the measure of ∠B.