Question

what is m∠1?
41°
97°
m∠1 = \boxed{\space}°
submit

Explanation:

Step1: Find the third angle of the triangle

The sum of the interior angles of a triangle is \(180^\circ\). Let the third angle be \(x\). So, \(x + 41^\circ+ 97^\circ= 180^\circ\). Solving for \(x\), we get \(x = 180^\circ-(41^\circ + 97^\circ)=180^\circ - 138^\circ = 42^\circ\).

Step2: Find \(m\angle1\)

\(\angle1\) and the third angle of the triangle are supplementary (they form a linear pair), so their sum is \(180^\circ\). Let \(m\angle1 = y\). Then \(y+42^\circ = 180^\circ\), so \(y = 180^\circ - 42^\circ=138^\circ\).

Answer:

\(138\)