Question

find the m∠s. =

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.

x =

∠a =

what is the value of x? x =

1. find eg =

6.

measure of ∠b and ∠e?

what is the measure of ∠xyz? what is the measure

∠e =

∠xyz =

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. In \(\triangle RST\), \(\angle JRS\) is an exterior angle. So, \(m\angle JRS=m\angle S + m\angle T\). Given \(m\angle JRS = 140^{\circ}\), \(m\angle S=(3x + 4)^{\circ}\), and \(m\angle T=(8x + 4)^{\circ}\). Then \(140=(3x + 4)+(8x + 4)\).

Step2: Simplify the equation

First, combine like terms: \(140=3x+4 + 8x+4\), which simplifies to \(140 = 11x+8\).

Step3: Solve for \(x\)

Subtract \(8\) from both sides of the equation: \(140−8=11x\), so \(132 = 11x\). Then divide both sides by \(11\): \(x=\frac{132}{11}=12\).

Step4: Find \(m\angle S\)

Substitute \(x = 12\) into the formula for \(m\angle S\). \(m\angle S=(3x + 4)^{\circ}\). Replace \(x\) with \(12\): \(m\angle S=(3\times12 + 4)^{\circ}=(36 + 4)^{\circ}=40^{\circ}\).

Answer:

\(40^{\circ}\)