One angle of a right triangle measures 63°. What is the measure of the other acute
angle?

Given that the triangle is a right angled triangle so one of its angles will be 90°. Then,

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Find x.

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With the angle sum property of a triangle, we can say that ⇨ angle 1 + angle 2 + angle 3 = 180° (the sum of measurements of all sides in a triangle will be equal to 180°).

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Solving...

angle 1 + angle 2 + angle 3 = 180°

90° + 63° + x = 180°

153° + x = 180°

x = 180° - 153°

x = 27°.

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The measure of the other acute angle is 27°.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.