Question

1. in a triangle, given: m <a = (5x + 7)

m<b = (12x - 13)° and m<c=(2x - 4)°
find x and the measure of ∠a.
5x+7
x = 10°
∠a = 57°
5(10)

1. find eg = 7

3x - 5
7x - 21
3x - 5 = 7x - 21
+5 +5
3x = 7x - 26
6.
what is the measure of ∠xyz? what is the measure of ∠ywx?
∠xyz =
∠ywx = 50

Explanation:

Step1: Set up the equation for the triangle's angle sum

The sum of angles in a triangle is \(180^{\circ}\). So, \((5x + 7)+(12x - 13)+(2x - 4)=180\).
Simplify the left - hand side: \(5x+7 + 12x-13+2x - 4=(5x + 12x+2x)+(7 - 13 - 4)=19x-10\).
The equation becomes \(19x-10 = 180\).

Step2: Solve for \(x\)

Add \(10\) to both sides of the equation \(19x-10+10 = 180 + 10\), which gives \(19x=190\).
Divide both sides by \(19\): \(x=\frac{190}{19}=10\).

Step3: Find the measure of \(\angle A\)

Substitute \(x = 10\) into the expression for \(\angle A\): \(\angle A=5x + 7\).
\(\angle A=5\times10+7=50 + 7=57^{\circ}\).

Answer:

\(x = 10\), \(\angle A=57^{\circ}\)