Question

in \\( \triangle hij, m \angle h = ( 6 x - 7 ) ^ { \circ }, m \angle i = ( x + 10 ) ^ { \circ }, \\) and \\( m \angle j = ( 3 x - 13 ) ^ { \circ } \\). find \\( m \angle h \\).

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle H+m\angle I + m\angle J=180^{\circ}\).
Substitute the given angle expressions: \((6x - 7)+(x + 10)+(3x-13)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((6x+x + 3x)+(-7 + 10-13)=180\).
\(10x-10 = 180\).

Step3: Solve for \(x\)

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

Step4: Find \(m\angle H\)

Substitute \(x = 19\) into the expression for \(m\angle H\): \(m\angle H=(6x - 7)^{\circ}\).
\(m\angle H=(6\times19-7)^{\circ}=(114 - 7)^{\circ}=101^{\circ}\).

Answer:

\(101^{\circ}\)