Question

in triangle abc, m∠a = 43° and m∠b = 85°. what is the m∠c? * (10 points)

5
in triangle jkl, if m∠j > 90°, then ∠k and ∠l are ____________. * (10 points)

obtuse
complementary
congruent
acute

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, for \(\triangle ABC\), we have \(m\angle A + m\angle B + m\angle C=180^{\circ}\).

Step2: Substitute the given values

We know that \(m\angle A = 43^{\circ}\) and \(m\angle B = 85^{\circ}\). Substituting these into the equation: \(43^{\circ}+85^{\circ}+m\angle C = 180^{\circ}\).

Step3: Solve for \(m\angle C\)

First, add \(43^{\circ}\) and \(85^{\circ}\): \(43 + 85=128\). Then the equation becomes \(128^{\circ}+m\angle C=180^{\circ}\). Subtract \(128^{\circ}\) from both sides: \(m\angle C=180^{\circ}- 128^{\circ}\).

Answer:

\(m\angle C = 52^{\circ}\)