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Problem 43

(a)Let \(\mathrm{ABC}\) be a right triangle with $\mathrm{m} \angle \mathrm{BCA}=90^{\circ}$ and \(\mathrm{m} \angle \mathrm{CAB}=30^{\circ}\). What is $\mathrm{m} \angle \mathrm{ABC} ?$ (b) Prove that in a right triangle the sum of the measures of the angles adjacent to the hypotenuse is \(90^{\circ}\).

Expert verified

\(m \angle ABC = 60^{\circ}\) and the sum of the measures of the angles adjacent to the hypotenuse in a right triangle is always equal to \(90^{\circ}\).

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Chapter 4

In $\triangle \mathrm{ABC}, \underline{\mathrm{AC}} \cong \underline{\mathrm{BC}}$. The measure of an exterior angle of vertex \(\mathrm{C}\) is represented by \(5 \mathrm{x}+10^{\circ}\). If $\angle \mathrm{A}\( measures \)30^{\circ}\(, find the value of \)\mathrm{x}$.

Chapter 4

Prove that each angle of an equilateral triangle has measure \(60^{\circ}\).

Chapter 4

The measure of the vertex angle of an Isosceles triangle exceeds the measure of each base angle by \(30^{\circ}\). Find the value of each angle of the triangle.

Chapter 4

Prove that a scalene triangle has has no 2 angles congruent.

Chapter 4

Prove that a triangle can have, at most, one obtuse angle.

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