Question

question 1 (multiple choice worth 1 points)
(07.02 mc)
the vertices of triangle hij lie on circle k, as shown.
if ( mangle ihj ) is ( 42^{circ} ), what is ( mangle ijh )?
( 45^{circ} )
( 48^{circ} )
( 138^{circ} )
( 228^{circ} )

Explanation:

Step1: Recall the property of a semicircle

An angle inscribed in a semicircle is a right angle. So, $\angle IJH = 90^{\circ}$.

Step2: Use the angle - sum property of a triangle

In $\triangle IJH$, we know that the sum of angles in a triangle is $180^{\circ}$. Let $\angle IHJ = 42^{\circ}$ and $\angle IJH=90^{\circ}$. Then, using the formula $\angle JIH+\angle IHJ+\angle IJH = 180^{\circ}$. We want to find $\angle JIH$. So, $\angle JIH=180^{\circ}-\angle IHJ - \angle IJH$.
Substitute the values: $\angle JIH=180^{\circ}- 42^{\circ}-90^{\circ}$.
Calculate: $\angle JIH = 48^{\circ}$.

Answer:

$48^{\circ}$ (corresponding to the option $\boldsymbol{48^{\circ}}$)